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Simplifying 4x3 + 14x2 + -15x = 0 Reorder the terms: -15x + 14x2 + 4x3 = 0 Solving -15x + 14x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-15 + 14x + 4x2) = 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 '(-15 + 14x + 4x2)' equal to zero and attempt to solve: Simplifying -15 + 14x + 4x2 = 0 Solving -15 + 14x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 3.5x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 3.5x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 3.5x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 3.5x + x2 = 0 + 3.75 3.5x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 3.5x + x2 = 3.75 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 3.75 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 3.75 + 3.0625 Combine like terms: 3.75 + 3.0625 = 6.8125 3.0625 + 3.5x + x2 = 6.8125 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 6.8125 Calculate the square root of the right side: 2.610076627 Break this problem into two subproblems by setting (x + 1.75) equal to 2.610076627 and -2.610076627.Subproblem 1
x + 1.75 = 2.610076627 Simplifying x + 1.75 = 2.610076627 Reorder the terms: 1.75 + x = 2.610076627 Solving 1.75 + x = 2.610076627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 2.610076627 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.610076627 + -1.75 x = 2.610076627 + -1.75 Combine like terms: 2.610076627 + -1.75 = 0.860076627 x = 0.860076627 Simplifying x = 0.860076627Subproblem 2
x + 1.75 = -2.610076627 Simplifying x + 1.75 = -2.610076627 Reorder the terms: 1.75 + x = -2.610076627 Solving 1.75 + x = -2.610076627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -2.610076627 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.610076627 + -1.75 x = -2.610076627 + -1.75 Combine like terms: -2.610076627 + -1.75 = -4.360076627 x = -4.360076627 Simplifying x = -4.360076627Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.860076627, -4.360076627}Solution
x = {0, 0.860076627, -4.360076627}
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