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Simplifying -5x2(3x2 + -3x + -7) = 0 Reorder the terms: -5x2(-7 + -3x + 3x2) = 0 (-7 * -5x2 + -3x * -5x2 + 3x2 * -5x2) = 0 (35x2 + 15x3 + -15x4) = 0 Solving 35x2 + 15x3 + -15x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x2'. 5x2(7 + 3x + -3x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(7 + 3x + -3x2)' equal to zero and attempt to solve: Simplifying 7 + 3x + -3x2 = 0 Solving 7 + 3x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.333333333 + -1x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -1x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -1x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -1x + x2 = 0 + 2.333333333 -1x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -1x + x2 = 2.333333333 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.333333333 + 0.25 Combine like terms: 2.333333333 + 0.25 = 2.583333333 0.25 + -1x + x2 = 2.583333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.583333333 Calculate the square root of the right side: 1.607275127 Break this problem into two subproblems by setting (x + -0.5) equal to 1.607275127 and -1.607275127.Subproblem 1
x + -0.5 = 1.607275127 Simplifying x + -0.5 = 1.607275127 Reorder the terms: -0.5 + x = 1.607275127 Solving -0.5 + x = 1.607275127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.607275127 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.607275127 + 0.5 x = 1.607275127 + 0.5 Combine like terms: 1.607275127 + 0.5 = 2.107275127 x = 2.107275127 Simplifying x = 2.107275127Subproblem 2
x + -0.5 = -1.607275127 Simplifying x + -0.5 = -1.607275127 Reorder the terms: -0.5 + x = -1.607275127 Solving -0.5 + x = -1.607275127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.607275127 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.607275127 + 0.5 x = -1.607275127 + 0.5 Combine like terms: -1.607275127 + 0.5 = -1.107275127 x = -1.107275127 Simplifying x = -1.107275127Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.107275127, -1.107275127}Solution
x = {0, 2.107275127, -1.107275127}
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