175.000+55.00x*1.00x=35.000+1680.00x

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Solution for 175.000+55.00x*1.00x=35.000+1680.00x equation:


Simplifying
175.000 + 55.00x * 1.00x = 35.000 + 1680.00x

Reorder the terms for easier multiplication:
175.000 + 55.00 * 1.00x * x = 35.000 + 1680.00x

Multiply 55.00 * 1.00
175.000 + 55x * x = 35.000 + 1680.00x

Multiply x * x
175.000 + 55x2 = 35.000 + 1680.00x

Solving
175.000 + 55x2 = 35.000 + 1680.00x

Solving for variable 'x'.

Reorder the terms:
175.000 + -35.000 + -1680.00x + 55x2 = 35.000 + 1680.00x + -35.000 + -1680.00x

Combine like terms: 175.000 + -35.000 = 140
140 + -1680.00x + 55x2 = 35.000 + 1680.00x + -35.000 + -1680.00x

Reorder the terms:
140 + -1680.00x + 55x2 = 35.000 + -35.000 + 1680.00x + -1680.00x

Combine like terms: 35.000 + -35.000 = 0.000
140 + -1680.00x + 55x2 = 0.000 + 1680.00x + -1680.00x
140 + -1680.00x + 55x2 = 1680.00x + -1680.00x

Combine like terms: 1680.00x + -1680.00x = 0.00
140 + -1680.00x + 55x2 = 0.00

Factor out the Greatest Common Factor (GCF), '5'.
5(28 + -336x + 11x2) = 0.00

Ignore the factor 5.

Subproblem 1

Set the factor '(28 + -336x + 11x2)' equal to zero and attempt to solve: Simplifying 28 + -336x + 11x2 = 0 Solving 28 + -336x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 2.545454545 + -30.54545455x + x2 = 0 Move the constant term to the right: Add '-2.545454545' to each side of the equation. 2.545454545 + -30.54545455x + -2.545454545 + x2 = 0 + -2.545454545 Reorder the terms: 2.545454545 + -2.545454545 + -30.54545455x + x2 = 0 + -2.545454545 Combine like terms: 2.545454545 + -2.545454545 = 0.000000000 0.000000000 + -30.54545455x + x2 = 0 + -2.545454545 -30.54545455x + x2 = 0 + -2.545454545 Combine like terms: 0 + -2.545454545 = -2.545454545 -30.54545455x + x2 = -2.545454545 The x term is -30.54545455x. Take half its coefficient (-15.27272728). Square it (233.2561986) and add it to both sides. Add '233.2561986' to each side of the equation. -30.54545455x + 233.2561986 + x2 = -2.545454545 + 233.2561986 Reorder the terms: 233.2561986 + -30.54545455x + x2 = -2.545454545 + 233.2561986 Combine like terms: -2.545454545 + 233.2561986 = 230.710744055 233.2561986 + -30.54545455x + x2 = 230.710744055 Factor a perfect square on the left side: (x + -15.27272728)(x + -15.27272728) = 230.710744055 Calculate the square root of the right side: 15.189165351 Break this problem into two subproblems by setting (x + -15.27272728) equal to 15.189165351 and -15.189165351.

Subproblem 1

x + -15.27272728 = 15.189165351 Simplifying x + -15.27272728 = 15.189165351 Reorder the terms: -15.27272728 + x = 15.189165351 Solving -15.27272728 + x = 15.189165351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.27272728' to each side of the equation. -15.27272728 + 15.27272728 + x = 15.189165351 + 15.27272728 Combine like terms: -15.27272728 + 15.27272728 = 0.00000000 0.00000000 + x = 15.189165351 + 15.27272728 x = 15.189165351 + 15.27272728 Combine like terms: 15.189165351 + 15.27272728 = 30.461892631 x = 30.461892631 Simplifying x = 30.461892631

Subproblem 2

x + -15.27272728 = -15.189165351 Simplifying x + -15.27272728 = -15.189165351 Reorder the terms: -15.27272728 + x = -15.189165351 Solving -15.27272728 + x = -15.189165351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.27272728' to each side of the equation. -15.27272728 + 15.27272728 + x = -15.189165351 + 15.27272728 Combine like terms: -15.27272728 + 15.27272728 = 0.00000000 0.00000000 + x = -15.189165351 + 15.27272728 x = -15.189165351 + 15.27272728 Combine like terms: -15.189165351 + 15.27272728 = 0.083561929 x = 0.083561929 Simplifying x = 0.083561929

Solution

The solution to the problem is based on the solutions from the subproblems. x = {30.461892631, 0.083561929}

Solution

x = {30.461892631, 0.083561929}

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