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Simplifying (-6x2 + 10x + 8) + (-8x2 + 2x + 6) = 0 Reorder the terms: (8 + 10x + -6x2) + (-8x2 + 2x + 6) = 0 Remove parenthesis around (8 + 10x + -6x2) 8 + 10x + -6x2 + (-8x2 + 2x + 6) = 0 Reorder the terms: 8 + 10x + -6x2 + (6 + 2x + -8x2) = 0 Remove parenthesis around (6 + 2x + -8x2) 8 + 10x + -6x2 + 6 + 2x + -8x2 = 0 Reorder the terms: 8 + 6 + 10x + 2x + -6x2 + -8x2 = 0 Combine like terms: 8 + 6 = 14 14 + 10x + 2x + -6x2 + -8x2 = 0 Combine like terms: 10x + 2x = 12x 14 + 12x + -6x2 + -8x2 = 0 Combine like terms: -6x2 + -8x2 = -14x2 14 + 12x + -14x2 = 0 Solving 14 + 12x + -14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 6x + -7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 6x + -7x2)' equal to zero and attempt to solve: Simplifying 7 + 6x + -7x2 = 0 Solving 7 + 6x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.8571428571x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.8571428571x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.8571428571x + x2 = 0 + 1 -0.8571428571x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.8571428571x + x2 = 1 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = 1 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 1 + 0.1836734694 Combine like terms: 1 + 0.1836734694 = 1.1836734694 0.1836734694 + -0.8571428571x + x2 = 1.1836734694 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 1.1836734694 Calculate the square root of the right side: 1.087967587 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 1.087967587 and -1.087967587.Subproblem 1
x + -0.4285714286 = 1.087967587 Simplifying x + -0.4285714286 = 1.087967587 Reorder the terms: -0.4285714286 + x = 1.087967587 Solving -0.4285714286 + x = 1.087967587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 1.087967587 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 1.087967587 + 0.4285714286 x = 1.087967587 + 0.4285714286 Combine like terms: 1.087967587 + 0.4285714286 = 1.5165390156 x = 1.5165390156 Simplifying x = 1.5165390156Subproblem 2
x + -0.4285714286 = -1.087967587 Simplifying x + -0.4285714286 = -1.087967587 Reorder the terms: -0.4285714286 + x = -1.087967587 Solving -0.4285714286 + x = -1.087967587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -1.087967587 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -1.087967587 + 0.4285714286 x = -1.087967587 + 0.4285714286 Combine like terms: -1.087967587 + 0.4285714286 = -0.6593961584 x = -0.6593961584 Simplifying x = -0.6593961584Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5165390156, -0.6593961584}Solution
x = {1.5165390156, -0.6593961584}
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