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Simplifying x2 + -10x + -2 = 9x + 4 Reorder the terms: -2 + -10x + x2 = 9x + 4 Reorder the terms: -2 + -10x + x2 = 4 + 9x Solving -2 + -10x + x2 = 4 + 9x Solving for variable 'x'. Reorder the terms: -2 + -4 + -10x + -9x + x2 = 4 + 9x + -4 + -9x Combine like terms: -2 + -4 = -6 -6 + -10x + -9x + x2 = 4 + 9x + -4 + -9x Combine like terms: -10x + -9x = -19x -6 + -19x + x2 = 4 + 9x + -4 + -9x Reorder the terms: -6 + -19x + x2 = 4 + -4 + 9x + -9x Combine like terms: 4 + -4 = 0 -6 + -19x + x2 = 0 + 9x + -9x -6 + -19x + x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -6 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -19x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -19x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -19x + x2 = 0 + 6 -19x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -19x + x2 = 6 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 6 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 6 + 90.25 Combine like terms: 6 + 90.25 = 96.25 90.25 + -19x + x2 = 96.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (x + -9.5) equal to 9.810708435 and -9.810708435.Subproblem 1
x + -9.5 = 9.810708435 Simplifying x + -9.5 = 9.810708435 Reorder the terms: -9.5 + x = 9.810708435 Solving -9.5 + x = 9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 9.810708435 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 9.810708435 + 9.5 x = 9.810708435 + 9.5 Combine like terms: 9.810708435 + 9.5 = 19.310708435 x = 19.310708435 Simplifying x = 19.310708435Subproblem 2
x + -9.5 = -9.810708435 Simplifying x + -9.5 = -9.810708435 Reorder the terms: -9.5 + x = -9.810708435 Solving -9.5 + x = -9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -9.810708435 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -9.810708435 + 9.5 x = -9.810708435 + 9.5 Combine like terms: -9.810708435 + 9.5 = -0.310708435 x = -0.310708435 Simplifying x = -0.310708435Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.310708435, -0.310708435}
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