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Simplifying 7x2 + 62x = 135 Reorder the terms: 62x + 7x2 = 135 Solving 62x + 7x2 = 135 Solving for variable 'x'. Reorder the terms: -135 + 62x + 7x2 = 135 + -135 Combine like terms: 135 + -135 = 0 -135 + 62x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -19.28571429 + 8.857142857x + x2 = 0 Move the constant term to the right: Add '19.28571429' to each side of the equation. -19.28571429 + 8.857142857x + 19.28571429 + x2 = 0 + 19.28571429 Reorder the terms: -19.28571429 + 19.28571429 + 8.857142857x + x2 = 0 + 19.28571429 Combine like terms: -19.28571429 + 19.28571429 = 0.00000000 0.00000000 + 8.857142857x + x2 = 0 + 19.28571429 8.857142857x + x2 = 0 + 19.28571429 Combine like terms: 0 + 19.28571429 = 19.28571429 8.857142857x + x2 = 19.28571429 The x term is 8.857142857x. Take half its coefficient (4.428571429). Square it (19.61224490) and add it to both sides. Add '19.61224490' to each side of the equation. 8.857142857x + 19.61224490 + x2 = 19.28571429 + 19.61224490 Reorder the terms: 19.61224490 + 8.857142857x + x2 = 19.28571429 + 19.61224490 Combine like terms: 19.28571429 + 19.61224490 = 38.89795919 19.61224490 + 8.857142857x + x2 = 38.89795919 Factor a perfect square on the left side: (x + 4.428571429)(x + 4.428571429) = 38.89795919 Calculate the square root of the right side: 6.236822844 Break this problem into two subproblems by setting (x + 4.428571429) equal to 6.236822844 and -6.236822844.Subproblem 1
x + 4.428571429 = 6.236822844 Simplifying x + 4.428571429 = 6.236822844 Reorder the terms: 4.428571429 + x = 6.236822844 Solving 4.428571429 + x = 6.236822844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.428571429' to each side of the equation. 4.428571429 + -4.428571429 + x = 6.236822844 + -4.428571429 Combine like terms: 4.428571429 + -4.428571429 = 0.000000000 0.000000000 + x = 6.236822844 + -4.428571429 x = 6.236822844 + -4.428571429 Combine like terms: 6.236822844 + -4.428571429 = 1.808251415 x = 1.808251415 Simplifying x = 1.808251415Subproblem 2
x + 4.428571429 = -6.236822844 Simplifying x + 4.428571429 = -6.236822844 Reorder the terms: 4.428571429 + x = -6.236822844 Solving 4.428571429 + x = -6.236822844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.428571429' to each side of the equation. 4.428571429 + -4.428571429 + x = -6.236822844 + -4.428571429 Combine like terms: 4.428571429 + -4.428571429 = 0.000000000 0.000000000 + x = -6.236822844 + -4.428571429 x = -6.236822844 + -4.428571429 Combine like terms: -6.236822844 + -4.428571429 = -10.665394273 x = -10.665394273 Simplifying x = -10.665394273Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.808251415, -10.665394273}
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