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Simplifying (x2 + -8x + 7) + -1(2x2 + -5x + -6) = 0 Reorder the terms: (7 + -8x + x2) + -1(2x2 + -5x + -6) = 0 Remove parenthesis around (7 + -8x + x2) 7 + -8x + x2 + -1(2x2 + -5x + -6) = 0 Reorder the terms: 7 + -8x + x2 + -1(-6 + -5x + 2x2) = 0 7 + -8x + x2 + (-6 * -1 + -5x * -1 + 2x2 * -1) = 0 7 + -8x + x2 + (6 + 5x + -2x2) = 0 Reorder the terms: 7 + 6 + -8x + 5x + x2 + -2x2 = 0 Combine like terms: 7 + 6 = 13 13 + -8x + 5x + x2 + -2x2 = 0 Combine like terms: -8x + 5x = -3x 13 + -3x + x2 + -2x2 = 0 Combine like terms: x2 + -2x2 = -1x2 13 + -3x + -1x2 = 0 Solving 13 + -3x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + 3x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 3x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 3x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 3x + x2 = 0 + 13 3x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 3x + x2 = 13 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 13 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 13 + 2.25 Combine like terms: 13 + 2.25 = 15.25 2.25 + 3x + x2 = 15.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + 1.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + 1.5 = 3.905124838 Simplifying x + 1.5 = 3.905124838 Reorder the terms: 1.5 + x = 3.905124838 Solving 1.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.905124838 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.905124838 + -1.5 x = 3.905124838 + -1.5 Combine like terms: 3.905124838 + -1.5 = 2.405124838 x = 2.405124838 Simplifying x = 2.405124838Subproblem 2
x + 1.5 = -3.905124838 Simplifying x + 1.5 = -3.905124838 Reorder the terms: 1.5 + x = -3.905124838 Solving 1.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.905124838 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.905124838 + -1.5 x = -3.905124838 + -1.5 Combine like terms: -3.905124838 + -1.5 = -5.405124838 x = -5.405124838 Simplifying x = -5.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.405124838, -5.405124838}
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