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Simplifying 2(3x2 + -5x) + 4x2(7 + x) = 0 Reorder the terms: 2(-5x + 3x2) + 4x2(7 + x) = 0 (-5x * 2 + 3x2 * 2) + 4x2(7 + x) = 0 (-10x + 6x2) + 4x2(7 + x) = 0 -10x + 6x2 + (7 * 4x2 + x * 4x2) = 0 -10x + 6x2 + (28x2 + 4x3) = 0 Combine like terms: 6x2 + 28x2 = 34x2 -10x + 34x2 + 4x3 = 0 Solving -10x + 34x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-5 + 17x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-5 + 17x + 2x2)' equal to zero and attempt to solve: Simplifying -5 + 17x + 2x2 = 0 Solving -5 + 17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 8.5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 8.5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 8.5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 8.5x + x2 = 0 + 2.5 8.5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 8.5x + x2 = 2.5 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 2.5 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 2.5 + 18.0625 Combine like terms: 2.5 + 18.0625 = 20.5625 18.0625 + 8.5x + x2 = 20.5625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (x + 4.25) equal to 4.534589287 and -4.534589287.Subproblem 1
x + 4.25 = 4.534589287 Simplifying x + 4.25 = 4.534589287 Reorder the terms: 4.25 + x = 4.534589287 Solving 4.25 + x = 4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 4.534589287 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 4.534589287 + -4.25 x = 4.534589287 + -4.25 Combine like terms: 4.534589287 + -4.25 = 0.284589287 x = 0.284589287 Simplifying x = 0.284589287Subproblem 2
x + 4.25 = -4.534589287 Simplifying x + 4.25 = -4.534589287 Reorder the terms: 4.25 + x = -4.534589287 Solving 4.25 + x = -4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -4.534589287 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -4.534589287 + -4.25 x = -4.534589287 + -4.25 Combine like terms: -4.534589287 + -4.25 = -8.784589287 x = -8.784589287 Simplifying x = -8.784589287Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.284589287, -8.784589287}Solution
x = {0, 0.284589287, -8.784589287}
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