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Simplifying (-7x2 + 4x + 7) + -1(-8x + 2) = 0 Reorder the terms: (7 + 4x + -7x2) + -1(-8x + 2) = 0 Remove parenthesis around (7 + 4x + -7x2) 7 + 4x + -7x2 + -1(-8x + 2) = 0 Reorder the terms: 7 + 4x + -7x2 + -1(2 + -8x) = 0 7 + 4x + -7x2 + (2 * -1 + -8x * -1) = 0 7 + 4x + -7x2 + (-2 + 8x) = 0 Reorder the terms: 7 + -2 + 4x + 8x + -7x2 = 0 Combine like terms: 7 + -2 = 5 5 + 4x + 8x + -7x2 = 0 Combine like terms: 4x + 8x = 12x 5 + 12x + -7x2 = 0 Solving 5 + 12x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.7142857143 + -1.714285714x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -1.714285714x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -1.714285714x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -1.714285714x + x2 = 0 + 0.7142857143 -1.714285714x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -1.714285714x + x2 = 0.7142857143 The x term is -1.714285714x. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714x + 0.7346938773 + x2 = 0.7142857143 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714x + x2 = 0.7142857143 + 0.7346938773 Combine like terms: 0.7142857143 + 0.7346938773 = 1.4489795916 0.7346938773 + -1.714285714x + x2 = 1.4489795916 Factor a perfect square on the left side: (x + -0.857142857)(x + -0.857142857) = 1.4489795916 Calculate the square root of the right side: 1.203735682 Break this problem into two subproblems by setting (x + -0.857142857) equal to 1.203735682 and -1.203735682.Subproblem 1
x + -0.857142857 = 1.203735682 Simplifying x + -0.857142857 = 1.203735682 Reorder the terms: -0.857142857 + x = 1.203735682 Solving -0.857142857 + x = 1.203735682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = 1.203735682 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 1.203735682 + 0.857142857 x = 1.203735682 + 0.857142857 Combine like terms: 1.203735682 + 0.857142857 = 2.060878539 x = 2.060878539 Simplifying x = 2.060878539Subproblem 2
x + -0.857142857 = -1.203735682 Simplifying x + -0.857142857 = -1.203735682 Reorder the terms: -0.857142857 + x = -1.203735682 Solving -0.857142857 + x = -1.203735682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = -1.203735682 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -1.203735682 + 0.857142857 x = -1.203735682 + 0.857142857 Combine like terms: -1.203735682 + 0.857142857 = -0.346592825 x = -0.346592825 Simplifying x = -0.346592825Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.060878539, -0.346592825}
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