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Simplifying 5x(2x + -8) + -2 = 5(x + -3) + 3 Reorder the terms: 5x(-8 + 2x) + -2 = 5(x + -3) + 3 (-8 * 5x + 2x * 5x) + -2 = 5(x + -3) + 3 (-40x + 10x2) + -2 = 5(x + -3) + 3 Reorder the terms: -2 + -40x + 10x2 = 5(x + -3) + 3 Reorder the terms: -2 + -40x + 10x2 = 5(-3 + x) + 3 -2 + -40x + 10x2 = (-3 * 5 + x * 5) + 3 -2 + -40x + 10x2 = (-15 + 5x) + 3 Reorder the terms: -2 + -40x + 10x2 = -15 + 3 + 5x Combine like terms: -15 + 3 = -12 -2 + -40x + 10x2 = -12 + 5x Solving -2 + -40x + 10x2 = -12 + 5x Solving for variable 'x'. Reorder the terms: -2 + 12 + -40x + -5x + 10x2 = -12 + 5x + 12 + -5x Combine like terms: -2 + 12 = 10 10 + -40x + -5x + 10x2 = -12 + 5x + 12 + -5x Combine like terms: -40x + -5x = -45x 10 + -45x + 10x2 = -12 + 5x + 12 + -5x Reorder the terms: 10 + -45x + 10x2 = -12 + 12 + 5x + -5x Combine like terms: -12 + 12 = 0 10 + -45x + 10x2 = 0 + 5x + -5x 10 + -45x + 10x2 = 5x + -5x Combine like terms: 5x + -5x = 0 10 + -45x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -9x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -9x + 2x2)' equal to zero and attempt to solve: Simplifying 2 + -9x + 2x2 = 0 Solving 2 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + -4.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -4.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.5x + x2 = 0 + -1 -4.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.5x + x2 = -1 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -1 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -1 + 5.0625 Combine like terms: -1 + 5.0625 = 4.0625 5.0625 + -4.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + -2.25) equal to 2.015564437 and -2.015564437.Subproblem 1
x + -2.25 = 2.015564437 Simplifying x + -2.25 = 2.015564437 Reorder the terms: -2.25 + x = 2.015564437 Solving -2.25 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.015564437 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.015564437 + 2.25 x = 2.015564437 + 2.25 Combine like terms: 2.015564437 + 2.25 = 4.265564437 x = 4.265564437 Simplifying x = 4.265564437Subproblem 2
x + -2.25 = -2.015564437 Simplifying x + -2.25 = -2.015564437 Reorder the terms: -2.25 + x = -2.015564437 Solving -2.25 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.015564437 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.015564437 + 2.25 x = -2.015564437 + 2.25 Combine like terms: -2.015564437 + 2.25 = 0.234435563 x = 0.234435563 Simplifying x = 0.234435563Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.265564437, 0.234435563}Solution
x = {4.265564437, 0.234435563}
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