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Simplifying 2x + -5x(3x + -10) = 7x + -5 Reorder the terms: 2x + -5x(-10 + 3x) = 7x + -5 2x + (-10 * -5x + 3x * -5x) = 7x + -5 2x + (50x + -15x2) = 7x + -5 Combine like terms: 2x + 50x = 52x 52x + -15x2 = 7x + -5 Reorder the terms: 52x + -15x2 = -5 + 7x Solving 52x + -15x2 = -5 + 7x Solving for variable 'x'. Reorder the terms: 5 + 52x + -7x + -15x2 = -5 + 7x + 5 + -7x Combine like terms: 52x + -7x = 45x 5 + 45x + -15x2 = -5 + 7x + 5 + -7x Reorder the terms: 5 + 45x + -15x2 = -5 + 5 + 7x + -7x Combine like terms: -5 + 5 = 0 5 + 45x + -15x2 = 0 + 7x + -7x 5 + 45x + -15x2 = 7x + -7x Combine like terms: 7x + -7x = 0 5 + 45x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 9x + -3x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + 9x + -3x2)' equal to zero and attempt to solve: Simplifying 1 + 9x + -3x2 = 0 Solving 1 + 9x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.3333333333 + -3x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -3x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -3x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + 0.3333333333 -3x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -3x + x2 = 0.3333333333 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 0.3333333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.3333333333 + 2.25 Combine like terms: 0.3333333333 + 2.25 = 2.5833333333 2.25 + -3x + x2 = 2.5833333333 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.5833333333 Calculate the square root of the right side: 1.607275127 Break this problem into two subproblems by setting (x + -1.5) equal to 1.607275127 and -1.607275127.Subproblem 1
x + -1.5 = 1.607275127 Simplifying x + -1.5 = 1.607275127 Reorder the terms: -1.5 + x = 1.607275127 Solving -1.5 + x = 1.607275127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.607275127 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.607275127 + 1.5 x = 1.607275127 + 1.5 Combine like terms: 1.607275127 + 1.5 = 3.107275127 x = 3.107275127 Simplifying x = 3.107275127Subproblem 2
x + -1.5 = -1.607275127 Simplifying x + -1.5 = -1.607275127 Reorder the terms: -1.5 + x = -1.607275127 Solving -1.5 + x = -1.607275127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.607275127 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.607275127 + 1.5 x = -1.607275127 + 1.5 Combine like terms: -1.607275127 + 1.5 = -0.107275127 x = -0.107275127 Simplifying x = -0.107275127Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.107275127, -0.107275127}Solution
x = {3.107275127, -0.107275127}
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