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Simplifying 25x3 + 16x2 = 12x Reorder the terms: 16x2 + 25x3 = 12x Solving 16x2 + 25x3 = 12x Solving for variable 'x'. Reorder the terms: -12x + 16x2 + 25x3 = 12x + -12x Combine like terms: 12x + -12x = 0 -12x + 16x2 + 25x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-12 + 16x + 25x2) = 0Subproblem 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 '(-12 + 16x + 25x2)' equal to zero and attempt to solve: Simplifying -12 + 16x + 25x2 = 0 Solving -12 + 16x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.48 + 0.64x + x2 = 0 Move the constant term to the right: Add '0.48' to each side of the equation. -0.48 + 0.64x + 0.48 + x2 = 0 + 0.48 Reorder the terms: -0.48 + 0.48 + 0.64x + x2 = 0 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + 0.64x + x2 = 0 + 0.48 0.64x + x2 = 0 + 0.48 Combine like terms: 0 + 0.48 = 0.48 0.64x + x2 = 0.48 The x term is 0.64x. Take half its coefficient (0.32). Square it (0.1024) and add it to both sides. Add '0.1024' to each side of the equation. 0.64x + 0.1024 + x2 = 0.48 + 0.1024 Reorder the terms: 0.1024 + 0.64x + x2 = 0.48 + 0.1024 Combine like terms: 0.48 + 0.1024 = 0.5824 0.1024 + 0.64x + x2 = 0.5824 Factor a perfect square on the left side: (x + 0.32)(x + 0.32) = 0.5824 Calculate the square root of the right side: 0.763151361 Break this problem into two subproblems by setting (x + 0.32) equal to 0.763151361 and -0.763151361.Subproblem 1
x + 0.32 = 0.763151361 Simplifying x + 0.32 = 0.763151361 Reorder the terms: 0.32 + x = 0.763151361 Solving 0.32 + x = 0.763151361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.32' to each side of the equation. 0.32 + -0.32 + x = 0.763151361 + -0.32 Combine like terms: 0.32 + -0.32 = 0.00 0.00 + x = 0.763151361 + -0.32 x = 0.763151361 + -0.32 Combine like terms: 0.763151361 + -0.32 = 0.443151361 x = 0.443151361 Simplifying x = 0.443151361Subproblem 2
x + 0.32 = -0.763151361 Simplifying x + 0.32 = -0.763151361 Reorder the terms: 0.32 + x = -0.763151361 Solving 0.32 + x = -0.763151361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.32' to each side of the equation. 0.32 + -0.32 + x = -0.763151361 + -0.32 Combine like terms: 0.32 + -0.32 = 0.00 0.00 + x = -0.763151361 + -0.32 x = -0.763151361 + -0.32 Combine like terms: -0.763151361 + -0.32 = -1.083151361 x = -1.083151361 Simplifying x = -1.083151361Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.443151361, -1.083151361}Solution
x = {0, 0.443151361, -1.083151361}
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