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Simplifying 10x2 + -38x + -16 = 0 Reorder the terms: -16 + -38x + 10x2 = 0 Solving -16 + -38x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -19x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -19x + 5x2)' equal to zero and attempt to solve: Simplifying -8 + -19x + 5x2 = 0 Solving -8 + -19x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + -3.8x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -3.8x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -3.8x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -3.8x + x2 = 0 + 1.6 -3.8x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -3.8x + x2 = 1.6 The x term is -3.8x. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8x + 3.61 + x2 = 1.6 + 3.61 Reorder the terms: 3.61 + -3.8x + x2 = 1.6 + 3.61 Combine like terms: 1.6 + 3.61 = 5.21 3.61 + -3.8x + x2 = 5.21 Factor a perfect square on the left side: (x + -1.9)(x + -1.9) = 5.21 Calculate the square root of the right side: 2.282542442 Break this problem into two subproblems by setting (x + -1.9) equal to 2.282542442 and -2.282542442.Subproblem 1
x + -1.9 = 2.282542442 Simplifying x + -1.9 = 2.282542442 Reorder the terms: -1.9 + x = 2.282542442 Solving -1.9 + x = 2.282542442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = 2.282542442 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = 2.282542442 + 1.9 x = 2.282542442 + 1.9 Combine like terms: 2.282542442 + 1.9 = 4.182542442 x = 4.182542442 Simplifying x = 4.182542442Subproblem 2
x + -1.9 = -2.282542442 Simplifying x + -1.9 = -2.282542442 Reorder the terms: -1.9 + x = -2.282542442 Solving -1.9 + x = -2.282542442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = -2.282542442 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = -2.282542442 + 1.9 x = -2.282542442 + 1.9 Combine like terms: -2.282542442 + 1.9 = -0.382542442 x = -0.382542442 Simplifying x = -0.382542442Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.182542442, -0.382542442}Solution
x = {4.182542442, -0.382542442}
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