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Simplifying (7x + -6)(7x + -6) = 55 Reorder the terms: (-6 + 7x)(7x + -6) = 55 Reorder the terms: (-6 + 7x)(-6 + 7x) = 55 Multiply (-6 + 7x) * (-6 + 7x) (-6(-6 + 7x) + 7x * (-6 + 7x)) = 55 ((-6 * -6 + 7x * -6) + 7x * (-6 + 7x)) = 55 ((36 + -42x) + 7x * (-6 + 7x)) = 55 (36 + -42x + (-6 * 7x + 7x * 7x)) = 55 (36 + -42x + (-42x + 49x2)) = 55 Combine like terms: -42x + -42x = -84x (36 + -84x + 49x2) = 55 Solving 36 + -84x + 49x2 = 55 Solving for variable 'x'. Reorder the terms: 36 + -55 + -84x + 49x2 = 55 + -55 Combine like terms: 36 + -55 = -19 -19 + -84x + 49x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -19 + -84x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.387755102 + -1.714285714x + x2 = 0 Move the constant term to the right: Add '0.387755102' to each side of the equation. -0.387755102 + -1.714285714x + 0.387755102 + x2 = 0 + 0.387755102 Reorder the terms: -0.387755102 + 0.387755102 + -1.714285714x + x2 = 0 + 0.387755102 Combine like terms: -0.387755102 + 0.387755102 = 0.000000000 0.000000000 + -1.714285714x + x2 = 0 + 0.387755102 -1.714285714x + x2 = 0 + 0.387755102 Combine like terms: 0 + 0.387755102 = 0.387755102 -1.714285714x + x2 = 0.387755102 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 = 0.387755102 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714x + x2 = 0.387755102 + 0.7346938773 Combine like terms: 0.387755102 + 0.7346938773 = 1.1224489793 0.7346938773 + -1.714285714x + x2 = 1.1224489793 Factor a perfect square on the left side: (x + -0.857142857)(x + -0.857142857) = 1.1224489793 Calculate the square root of the right side: 1.059456927 Break this problem into two subproblems by setting (x + -0.857142857) equal to 1.059456927 and -1.059456927.Subproblem 1
x + -0.857142857 = 1.059456927 Simplifying x + -0.857142857 = 1.059456927 Reorder the terms: -0.857142857 + x = 1.059456927 Solving -0.857142857 + x = 1.059456927 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 = 1.059456927 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 1.059456927 + 0.857142857 x = 1.059456927 + 0.857142857 Combine like terms: 1.059456927 + 0.857142857 = 1.916599784 x = 1.916599784 Simplifying x = 1.916599784Subproblem 2
x + -0.857142857 = -1.059456927 Simplifying x + -0.857142857 = -1.059456927 Reorder the terms: -0.857142857 + x = -1.059456927 Solving -0.857142857 + x = -1.059456927 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 = -1.059456927 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -1.059456927 + 0.857142857 x = -1.059456927 + 0.857142857 Combine like terms: -1.059456927 + 0.857142857 = -0.20231407 x = -0.20231407 Simplifying x = -0.20231407Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.916599784, -0.20231407}
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