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Simplifying 4x3 + -17x2 + -15x = 5x Reorder the terms: -15x + -17x2 + 4x3 = 5x Solving -15x + -17x2 + 4x3 = 5x Solving for variable 'x'. Reorder the terms: -15x + -5x + -17x2 + 4x3 = 5x + -5x Combine like terms: -15x + -5x = -20x -20x + -17x2 + 4x3 = 5x + -5x Combine like terms: 5x + -5x = 0 -20x + -17x2 + 4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-20 + -17x + 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 '(-20 + -17x + 4x2)' equal to zero and attempt to solve: Simplifying -20 + -17x + 4x2 = 0 Solving -20 + -17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5 + -4.25x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -4.25x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -4.25x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4.25x + x2 = 0 + 5 -4.25x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -4.25x + x2 = 5 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = 5 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = 5 + 4.515625 Combine like terms: 5 + 4.515625 = 9.515625 4.515625 + -4.25x + x2 = 9.515625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 9.515625 Calculate the square root of the right side: 3.08474067 Break this problem into two subproblems by setting (x + -2.125) equal to 3.08474067 and -3.08474067.Subproblem 1
x + -2.125 = 3.08474067 Simplifying x + -2.125 = 3.08474067 Reorder the terms: -2.125 + x = 3.08474067 Solving -2.125 + x = 3.08474067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 3.08474067 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 3.08474067 + 2.125 x = 3.08474067 + 2.125 Combine like terms: 3.08474067 + 2.125 = 5.20974067 x = 5.20974067 Simplifying x = 5.20974067Subproblem 2
x + -2.125 = -3.08474067 Simplifying x + -2.125 = -3.08474067 Reorder the terms: -2.125 + x = -3.08474067 Solving -2.125 + x = -3.08474067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -3.08474067 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -3.08474067 + 2.125 x = -3.08474067 + 2.125 Combine like terms: -3.08474067 + 2.125 = -0.95974067 x = -0.95974067 Simplifying x = -0.95974067Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.20974067, -0.95974067}Solution
x = {0, 5.20974067, -0.95974067}
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