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Simplifying 42x + -69x + 20 = 7x2 + -8 Reorder the terms: 20 + 42x + -69x = 7x2 + -8 Combine like terms: 42x + -69x = -27x 20 + -27x = 7x2 + -8 Reorder the terms: 20 + -27x = -8 + 7x2 Solving 20 + -27x = -8 + 7x2 Solving for variable 'x'. Reorder the terms: 20 + 8 + -27x + -7x2 = -8 + 7x2 + 8 + -7x2 Combine like terms: 20 + 8 = 28 28 + -27x + -7x2 = -8 + 7x2 + 8 + -7x2 Reorder the terms: 28 + -27x + -7x2 = -8 + 8 + 7x2 + -7x2 Combine like terms: -8 + 8 = 0 28 + -27x + -7x2 = 0 + 7x2 + -7x2 28 + -27x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 28 + -27x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -4 + 3.857142857x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 3.857142857x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 3.857142857x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3.857142857x + x2 = 0 + 4 3.857142857x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 3.857142857x + x2 = 4 The x term is 3.857142857x. Take half its coefficient (1.928571429). Square it (3.719387757) and add it to both sides. Add '3.719387757' to each side of the equation. 3.857142857x + 3.719387757 + x2 = 4 + 3.719387757 Reorder the terms: 3.719387757 + 3.857142857x + x2 = 4 + 3.719387757 Combine like terms: 4 + 3.719387757 = 7.719387757 3.719387757 + 3.857142857x + x2 = 7.719387757 Factor a perfect square on the left side: (x + 1.928571429)(x + 1.928571429) = 7.719387757 Calculate the square root of the right side: 2.77837862 Break this problem into two subproblems by setting (x + 1.928571429) equal to 2.77837862 and -2.77837862.Subproblem 1
x + 1.928571429 = 2.77837862 Simplifying x + 1.928571429 = 2.77837862 Reorder the terms: 1.928571429 + x = 2.77837862 Solving 1.928571429 + x = 2.77837862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.928571429' to each side of the equation. 1.928571429 + -1.928571429 + x = 2.77837862 + -1.928571429 Combine like terms: 1.928571429 + -1.928571429 = 0.000000000 0.000000000 + x = 2.77837862 + -1.928571429 x = 2.77837862 + -1.928571429 Combine like terms: 2.77837862 + -1.928571429 = 0.849807191 x = 0.849807191 Simplifying x = 0.849807191Subproblem 2
x + 1.928571429 = -2.77837862 Simplifying x + 1.928571429 = -2.77837862 Reorder the terms: 1.928571429 + x = -2.77837862 Solving 1.928571429 + x = -2.77837862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.928571429' to each side of the equation. 1.928571429 + -1.928571429 + x = -2.77837862 + -1.928571429 Combine like terms: 1.928571429 + -1.928571429 = 0.000000000 0.000000000 + x = -2.77837862 + -1.928571429 x = -2.77837862 + -1.928571429 Combine like terms: -2.77837862 + -1.928571429 = -4.706950049 x = -4.706950049 Simplifying x = -4.706950049Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.849807191, -4.706950049}
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