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Simplifying 2x * 2x * 2x + 10x * 10x + -28x = 0 Reorder the terms for easier multiplication: 2 * 2 * 2x * x * x + 10x * 10x + -28x = 0 Multiply 2 * 2 4 * 2x * x * x + 10x * 10x + -28x = 0 Multiply 4 * 2 8x * x * x + 10x * 10x + -28x = 0 Multiply x * x 8x2 * x + 10x * 10x + -28x = 0 Multiply x2 * x 8x3 + 10x * 10x + -28x = 0 Reorder the terms for easier multiplication: 8x3 + 10 * 10x * x + -28x = 0 Multiply 10 * 10 8x3 + 100x * x + -28x = 0 Multiply x * x 8x3 + 100x2 + -28x = 0 Reorder the terms: -28x + 100x2 + 8x3 = 0 Solving -28x + 100x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-7 + 25x + 2x2) = 0 Ignore the factor 4.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 '(-7 + 25x + 2x2)' equal to zero and attempt to solve: Simplifying -7 + 25x + 2x2 = 0 Solving -7 + 25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 12.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 12.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 12.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 12.5x + x2 = 0 + 3.5 12.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 12.5x + x2 = 3.5 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = 3.5 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 3.5 + 39.0625 Combine like terms: 3.5 + 39.0625 = 42.5625 39.0625 + 12.5x + x2 = 42.5625 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 42.5625 Calculate the square root of the right side: 6.523994175 Break this problem into two subproblems by setting (x + 6.25) equal to 6.523994175 and -6.523994175.Subproblem 1
x + 6.25 = 6.523994175 Simplifying x + 6.25 = 6.523994175 Reorder the terms: 6.25 + x = 6.523994175 Solving 6.25 + x = 6.523994175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 6.523994175 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 6.523994175 + -6.25 x = 6.523994175 + -6.25 Combine like terms: 6.523994175 + -6.25 = 0.273994175 x = 0.273994175 Simplifying x = 0.273994175Subproblem 2
x + 6.25 = -6.523994175 Simplifying x + 6.25 = -6.523994175 Reorder the terms: 6.25 + x = -6.523994175 Solving 6.25 + x = -6.523994175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -6.523994175 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -6.523994175 + -6.25 x = -6.523994175 + -6.25 Combine like terms: -6.523994175 + -6.25 = -12.773994175 x = -12.773994175 Simplifying x = -12.773994175Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.273994175, -12.773994175}Solution
x = {0, 0.273994175, -12.773994175}
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