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Simplifying x2 + -7x + 3 = 8x + -10 Reorder the terms: 3 + -7x + x2 = 8x + -10 Reorder the terms: 3 + -7x + x2 = -10 + 8x Solving 3 + -7x + x2 = -10 + 8x Solving for variable 'x'. Reorder the terms: 3 + 10 + -7x + -8x + x2 = -10 + 8x + 10 + -8x Combine like terms: 3 + 10 = 13 13 + -7x + -8x + x2 = -10 + 8x + 10 + -8x Combine like terms: -7x + -8x = -15x 13 + -15x + x2 = -10 + 8x + 10 + -8x Reorder the terms: 13 + -15x + x2 = -10 + 10 + 8x + -8x Combine like terms: -10 + 10 = 0 13 + -15x + x2 = 0 + 8x + -8x 13 + -15x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 13 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -15x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -15x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -15x + x2 = 0 + -13 -15x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -15x + x2 = -13 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -13 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -13 + 56.25 Combine like terms: -13 + 56.25 = 43.25 56.25 + -15x + x2 = 43.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (x + -7.5) equal to 6.576473219 and -6.576473219.Subproblem 1
x + -7.5 = 6.576473219 Simplifying x + -7.5 = 6.576473219 Reorder the terms: -7.5 + x = 6.576473219 Solving -7.5 + x = 6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 6.576473219 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.576473219 + 7.5 x = 6.576473219 + 7.5 Combine like terms: 6.576473219 + 7.5 = 14.076473219 x = 14.076473219 Simplifying x = 14.076473219Subproblem 2
x + -7.5 = -6.576473219 Simplifying x + -7.5 = -6.576473219 Reorder the terms: -7.5 + x = -6.576473219 Solving -7.5 + x = -6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -6.576473219 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.576473219 + 7.5 x = -6.576473219 + 7.5 Combine like terms: -6.576473219 + 7.5 = 0.923526781 x = 0.923526781 Simplifying x = 0.923526781Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.076473219, 0.923526781}
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