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Simplifying (6x2 + -5x + 8) + (-8x2 + -7x + 1) = 0 Reorder the terms: (8 + -5x + 6x2) + (-8x2 + -7x + 1) = 0 Remove parenthesis around (8 + -5x + 6x2) 8 + -5x + 6x2 + (-8x2 + -7x + 1) = 0 Reorder the terms: 8 + -5x + 6x2 + (1 + -7x + -8x2) = 0 Remove parenthesis around (1 + -7x + -8x2) 8 + -5x + 6x2 + 1 + -7x + -8x2 = 0 Reorder the terms: 8 + 1 + -5x + -7x + 6x2 + -8x2 = 0 Combine like terms: 8 + 1 = 9 9 + -5x + -7x + 6x2 + -8x2 = 0 Combine like terms: -5x + -7x = -12x 9 + -12x + 6x2 + -8x2 = 0 Combine like terms: 6x2 + -8x2 = -2x2 9 + -12x + -2x2 = 0 Solving 9 + -12x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + 6x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 6x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 6x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 6x + x2 = 0 + 4.5 6x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 6x + x2 = 4.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 4.5 + 9 Reorder the terms: 9 + 6x + x2 = 4.5 + 9 Combine like terms: 4.5 + 9 = 13.5 9 + 6x + x2 = 13.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (x + 3) equal to 3.674234614 and -3.674234614.Subproblem 1
x + 3 = 3.674234614 Simplifying x + 3 = 3.674234614 Reorder the terms: 3 + x = 3.674234614 Solving 3 + x = 3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.674234614 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.674234614 + -3 x = 3.674234614 + -3 Combine like terms: 3.674234614 + -3 = 0.674234614 x = 0.674234614 Simplifying x = 0.674234614Subproblem 2
x + 3 = -3.674234614 Simplifying x + 3 = -3.674234614 Reorder the terms: 3 + x = -3.674234614 Solving 3 + x = -3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.674234614 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.674234614 + -3 x = -3.674234614 + -3 Combine like terms: -3.674234614 + -3 = -6.674234614 x = -6.674234614 Simplifying x = -6.674234614Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.674234614, -6.674234614}
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