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Simplifying 10x + 3 + -1[2(x2 + -6) + 8] = 0 Reorder the terms: 10x + 3 + -1[2(-6 + x2) + 8] = 0 10x + 3 + -1[(-6 * 2 + x2 * 2) + 8] = 0 10x + 3 + -1[(-12 + 2x2) + 8] = 0 Reorder the terms: 10x + 3 + -1[-12 + 8 + 2x2] = 0 Combine like terms: -12 + 8 = -4 10x + 3 + -1[-4 + 2x2] = 0 10x + 3 + [-4 * -1 + 2x2 * -1] = 0 10x + 3 + [4 + -2x2] = 0 Reorder the terms: 3 + 4 + 10x + -2x2 = 0 Combine like terms: 3 + 4 = 7 7 + 10x + -2x2 = 0 Solving 7 + 10x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3.5 + -5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -5x + x2 = 0 + 3.5 -5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -5x + x2 = 3.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 3.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 3.5 + 6.25 Combine like terms: 3.5 + 6.25 = 9.75 6.25 + -5x + x2 = 9.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (x + -2.5) equal to 3.122498999 and -3.122498999.Subproblem 1
x + -2.5 = 3.122498999 Simplifying x + -2.5 = 3.122498999 Reorder the terms: -2.5 + x = 3.122498999 Solving -2.5 + x = 3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.122498999 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.122498999 + 2.5 x = 3.122498999 + 2.5 Combine like terms: 3.122498999 + 2.5 = 5.622498999 x = 5.622498999 Simplifying x = 5.622498999Subproblem 2
x + -2.5 = -3.122498999 Simplifying x + -2.5 = -3.122498999 Reorder the terms: -2.5 + x = -3.122498999 Solving -2.5 + x = -3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.122498999 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.122498999 + 2.5 x = -3.122498999 + 2.5 Combine like terms: -3.122498999 + 2.5 = -0.622498999 x = -0.622498999 Simplifying x = -0.622498999Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.622498999, -0.622498999}
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