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Simplifying 4(4x2 + -3x + -17) = 0 Reorder the terms: 4(-17 + -3x + 4x2) = 0 (-17 * 4 + -3x * 4 + 4x2 * 4) = 0 (-68 + -12x + 16x2) = 0 Solving -68 + -12x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-17 + -3x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-17 + -3x + 4x2)' equal to zero and attempt to solve: Simplifying -17 + -3x + 4x2 = 0 Solving -17 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + -0.75x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -0.75x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -0.75x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -0.75x + x2 = 0 + 4.25 -0.75x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -0.75x + x2 = 4.25 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 4.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 4.25 + 0.140625 Combine like terms: 4.25 + 0.140625 = 4.390625 0.140625 + -0.75x + x2 = 4.390625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (x + -0.375) equal to 2.095381827 and -2.095381827.Subproblem 1
x + -0.375 = 2.095381827 Simplifying x + -0.375 = 2.095381827 Reorder the terms: -0.375 + x = 2.095381827 Solving -0.375 + x = 2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 2.095381827 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 2.095381827 + 0.375 x = 2.095381827 + 0.375 Combine like terms: 2.095381827 + 0.375 = 2.470381827 x = 2.470381827 Simplifying x = 2.470381827Subproblem 2
x + -0.375 = -2.095381827 Simplifying x + -0.375 = -2.095381827 Reorder the terms: -0.375 + x = -2.095381827 Solving -0.375 + x = -2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -2.095381827 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -2.095381827 + 0.375 x = -2.095381827 + 0.375 Combine like terms: -2.095381827 + 0.375 = -1.720381827 x = -1.720381827 Simplifying x = -1.720381827Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.470381827, -1.720381827}Solution
x = {2.470381827, -1.720381827}
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