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Simplifying -2x2(4x2 + 5x + -3) = 0 Reorder the terms: -2x2(-3 + 5x + 4x2) = 0 (-3 * -2x2 + 5x * -2x2 + 4x2 * -2x2) = 0 (6x2 + -10x3 + -8x4) = 0 Solving 6x2 + -10x3 + -8x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(3 + -5x + -4x2) = 0 Ignore the factor 2.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 '(3 + -5x + -4x2)' equal to zero and attempt to solve: Simplifying 3 + -5x + -4x2 = 0 Solving 3 + -5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + 1.25x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 1.25x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 1.25x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 1.25x + x2 = 0 + 0.75 1.25x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 1.25x + x2 = 0.75 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 0.75 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 0.75 + 0.390625 Combine like terms: 0.75 + 0.390625 = 1.140625 0.390625 + 1.25x + x2 = 1.140625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + 0.625) equal to 1.068000468 and -1.068000468.Subproblem 1
x + 0.625 = 1.068000468 Simplifying x + 0.625 = 1.068000468 Reorder the terms: 0.625 + x = 1.068000468 Solving 0.625 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.068000468 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.068000468 + -0.625 x = 1.068000468 + -0.625 Combine like terms: 1.068000468 + -0.625 = 0.443000468 x = 0.443000468 Simplifying x = 0.443000468Subproblem 2
x + 0.625 = -1.068000468 Simplifying x + 0.625 = -1.068000468 Reorder the terms: 0.625 + x = -1.068000468 Solving 0.625 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.068000468 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.068000468 + -0.625 x = -1.068000468 + -0.625 Combine like terms: -1.068000468 + -0.625 = -1.693000468 x = -1.693000468 Simplifying x = -1.693000468Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.443000468, -1.693000468}Solution
x = {0, 0.443000468, -1.693000468}
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