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Simplifying (-6x + 8) + -1(x2 + x + -7) = 0 Reorder the terms: (8 + -6x) + -1(x2 + x + -7) = 0 Remove parenthesis around (8 + -6x) 8 + -6x + -1(x2 + x + -7) = 0 Reorder the terms: 8 + -6x + -1(-7 + x + x2) = 0 8 + -6x + (-7 * -1 + x * -1 + x2 * -1) = 0 8 + -6x + (7 + -1x + -1x2) = 0 Reorder the terms: 8 + 7 + -6x + -1x + -1x2 = 0 Combine like terms: 8 + 7 = 15 15 + -6x + -1x + -1x2 = 0 Combine like terms: -6x + -1x = -7x 15 + -7x + -1x2 = 0 Solving 15 + -7x + -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'. -15 + 7x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 7x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 7x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 7x + x2 = 0 + 15 7x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 7x + x2 = 15 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 15 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 15 + 12.25 Combine like terms: 15 + 12.25 = 27.25 12.25 + 7x + x2 = 27.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + 3.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + 3.5 = 5.220153254 Simplifying x + 3.5 = 5.220153254 Reorder the terms: 3.5 + x = 5.220153254 Solving 3.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.220153254 + -3.5 x = 5.220153254 + -3.5 Combine like terms: 5.220153254 + -3.5 = 1.720153254 x = 1.720153254 Simplifying x = 1.720153254Subproblem 2
x + 3.5 = -5.220153254 Simplifying x + 3.5 = -5.220153254 Reorder the terms: 3.5 + x = -5.220153254 Solving 3.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.220153254 + -3.5 x = -5.220153254 + -3.5 Combine like terms: -5.220153254 + -3.5 = -8.720153254 x = -8.720153254 Simplifying x = -8.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.720153254, -8.720153254}
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