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Simplifying 10x(7x + -7) = (8x + 6) Reorder the terms: 10x(-7 + 7x) = (8x + 6) (-7 * 10x + 7x * 10x) = (8x + 6) (-70x + 70x2) = (8x + 6) Reorder the terms: -70x + 70x2 = (6 + 8x) Remove parenthesis around (6 + 8x) -70x + 70x2 = 6 + 8x Solving -70x + 70x2 = 6 + 8x Solving for variable 'x'. Reorder the terms: -6 + -70x + -8x + 70x2 = 6 + 8x + -6 + -8x Combine like terms: -70x + -8x = -78x -6 + -78x + 70x2 = 6 + 8x + -6 + -8x Reorder the terms: -6 + -78x + 70x2 = 6 + -6 + 8x + -8x Combine like terms: 6 + -6 = 0 -6 + -78x + 70x2 = 0 + 8x + -8x -6 + -78x + 70x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -6 + -78x + 70x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -39x + 35x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -39x + 35x2)' equal to zero and attempt to solve: Simplifying -3 + -39x + 35x2 = 0 Solving -3 + -39x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.08571428571 + -1.114285714x + x2 = 0 Move the constant term to the right: Add '0.08571428571' to each side of the equation. -0.08571428571 + -1.114285714x + 0.08571428571 + x2 = 0 + 0.08571428571 Reorder the terms: -0.08571428571 + 0.08571428571 + -1.114285714x + x2 = 0 + 0.08571428571 Combine like terms: -0.08571428571 + 0.08571428571 = 0.00000000000 0.00000000000 + -1.114285714x + x2 = 0 + 0.08571428571 -1.114285714x + x2 = 0 + 0.08571428571 Combine like terms: 0 + 0.08571428571 = 0.08571428571 -1.114285714x + x2 = 0.08571428571 The x term is -1.114285714x. Take half its coefficient (-0.557142857). Square it (0.3104081631) and add it to both sides. Add '0.3104081631' to each side of the equation. -1.114285714x + 0.3104081631 + x2 = 0.08571428571 + 0.3104081631 Reorder the terms: 0.3104081631 + -1.114285714x + x2 = 0.08571428571 + 0.3104081631 Combine like terms: 0.08571428571 + 0.3104081631 = 0.39612244881 0.3104081631 + -1.114285714x + x2 = 0.39612244881 Factor a perfect square on the left side: (x + -0.557142857)(x + -0.557142857) = 0.39612244881 Calculate the square root of the right side: 0.629382593 Break this problem into two subproblems by setting (x + -0.557142857) equal to 0.629382593 and -0.629382593.Subproblem 1
x + -0.557142857 = 0.629382593 Simplifying x + -0.557142857 = 0.629382593 Reorder the terms: -0.557142857 + x = 0.629382593 Solving -0.557142857 + x = 0.629382593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.557142857' to each side of the equation. -0.557142857 + 0.557142857 + x = 0.629382593 + 0.557142857 Combine like terms: -0.557142857 + 0.557142857 = 0.000000000 0.000000000 + x = 0.629382593 + 0.557142857 x = 0.629382593 + 0.557142857 Combine like terms: 0.629382593 + 0.557142857 = 1.18652545 x = 1.18652545 Simplifying x = 1.18652545Subproblem 2
x + -0.557142857 = -0.629382593 Simplifying x + -0.557142857 = -0.629382593 Reorder the terms: -0.557142857 + x = -0.629382593 Solving -0.557142857 + x = -0.629382593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.557142857' to each side of the equation. -0.557142857 + 0.557142857 + x = -0.629382593 + 0.557142857 Combine like terms: -0.557142857 + 0.557142857 = 0.000000000 0.000000000 + x = -0.629382593 + 0.557142857 x = -0.629382593 + 0.557142857 Combine like terms: -0.629382593 + 0.557142857 = -0.072239736 x = -0.072239736 Simplifying x = -0.072239736Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.18652545, -0.072239736}Solution
x = {1.18652545, -0.072239736}
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