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Simplifying (-3x + 8) + -1(x2 + x + -7) = 0 Reorder the terms: (8 + -3x) + -1(x2 + x + -7) = 0 Remove parenthesis around (8 + -3x) 8 + -3x + -1(x2 + x + -7) = 0 Reorder the terms: 8 + -3x + -1(-7 + x + x2) = 0 8 + -3x + (-7 * -1 + x * -1 + x2 * -1) = 0 8 + -3x + (7 + -1x + -1x2) = 0 Reorder the terms: 8 + 7 + -3x + -1x + -1x2 = 0 Combine like terms: 8 + 7 = 15 15 + -3x + -1x + -1x2 = 0 Combine like terms: -3x + -1x = -4x 15 + -4x + -1x2 = 0 Solving 15 + -4x + -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 + 4x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 4x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 4x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4x + x2 = 0 + 15 4x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 4x + x2 = 15 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 15 + 4 Reorder the terms: 4 + 4x + x2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + 4x + x2 = 19 Factor a perfect square on the left side: (x + 2)(x + 2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 2) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 2 = 4.358898944 Simplifying x + 2 = 4.358898944 Reorder the terms: 2 + x = 4.358898944 Solving 2 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.358898944 + -2 x = 4.358898944 + -2 Combine like terms: 4.358898944 + -2 = 2.358898944 x = 2.358898944 Simplifying x = 2.358898944Subproblem 2
x + 2 = -4.358898944 Simplifying x + 2 = -4.358898944 Reorder the terms: 2 + x = -4.358898944 Solving 2 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.358898944 + -2 x = -4.358898944 + -2 Combine like terms: -4.358898944 + -2 = -6.358898944 x = -6.358898944 Simplifying x = -6.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.358898944, -6.358898944}
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