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Simplifying 25x2 + -15x + 35x3 = 0 Reorder the terms: -15x + 25x2 + 35x3 = 0 Solving -15x + 25x2 + 35x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(-3 + 5x + 7x2) = 0 Ignore the factor 5.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 '(-3 + 5x + 7x2)' equal to zero and attempt to solve: Simplifying -3 + 5x + 7x2 = 0 Solving -3 + 5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.7142857143x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 0.7142857143x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 0.7142857143x + x2 = 0 + 0.4285714286 0.7142857143x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 0.7142857143x + x2 = 0.4285714286 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = 0.4285714286 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 0.4285714286 + 0.1275510204 Combine like terms: 0.4285714286 + 0.1275510204 = 0.556122449 0.1275510204 + 0.7142857143x + x2 = 0.556122449 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 0.556122449 Calculate the square root of the right side: 0.745736179 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 0.745736179 and -0.745736179.Subproblem 1
x + 0.3571428572 = 0.745736179 Simplifying x + 0.3571428572 = 0.745736179 Reorder the terms: 0.3571428572 + x = 0.745736179 Solving 0.3571428572 + x = 0.745736179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 0.745736179 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 0.745736179 + -0.3571428572 x = 0.745736179 + -0.3571428572 Combine like terms: 0.745736179 + -0.3571428572 = 0.3885933218 x = 0.3885933218 Simplifying x = 0.3885933218Subproblem 2
x + 0.3571428572 = -0.745736179 Simplifying x + 0.3571428572 = -0.745736179 Reorder the terms: 0.3571428572 + x = -0.745736179 Solving 0.3571428572 + x = -0.745736179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -0.745736179 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -0.745736179 + -0.3571428572 x = -0.745736179 + -0.3571428572 Combine like terms: -0.745736179 + -0.3571428572 = -1.1028790362 x = -1.1028790362 Simplifying x = -1.1028790362Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3885933218, -1.1028790362}Solution
x = {0, 0.3885933218, -1.1028790362}
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