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Simplifying (x2 + -12) + (43 + -2x) = 90 Reorder the terms: (-12 + x2) + (43 + -2x) = 90 Remove parenthesis around (-12 + x2) -12 + x2 + (43 + -2x) = 90 Remove parenthesis around (43 + -2x) -12 + x2 + 43 + -2x = 90 Reorder the terms: -12 + 43 + -2x + x2 = 90 Combine like terms: -12 + 43 = 31 31 + -2x + x2 = 90 Solving 31 + -2x + x2 = 90 Solving for variable 'x'. Reorder the terms: 31 + -90 + -2x + x2 = 90 + -90 Combine like terms: 31 + -90 = -59 -59 + -2x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -59 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + -2x + 59 + x2 = 0 + 59 Reorder the terms: -59 + 59 + -2x + x2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + -2x + x2 = 0 + 59 -2x + x2 = 0 + 59 Combine like terms: 0 + 59 = 59 -2x + x2 = 59 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 59 + 1 Reorder the terms: 1 + -2x + x2 = 59 + 1 Combine like terms: 59 + 1 = 60 1 + -2x + x2 = 60 Factor a perfect square on the left side: (x + -1)(x + -1) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -1) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -1 = 7.745966692 Simplifying x + -1 = 7.745966692 Reorder the terms: -1 + x = 7.745966692 Solving -1 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 7.745966692 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.745966692 + 1 x = 7.745966692 + 1 Combine like terms: 7.745966692 + 1 = 8.745966692 x = 8.745966692 Simplifying x = 8.745966692Subproblem 2
x + -1 = -7.745966692 Simplifying x + -1 = -7.745966692 Reorder the terms: -1 + x = -7.745966692 Solving -1 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -7.745966692 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.745966692 + 1 x = -7.745966692 + 1 Combine like terms: -7.745966692 + 1 = -6.745966692 x = -6.745966692 Simplifying x = -6.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.745966692, -6.745966692}
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