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Simplifying 7x2 + 14x + -70 = -8 Reorder the terms: -70 + 14x + 7x2 = -8 Solving -70 + 14x + 7x2 = -8 Solving for variable 'x'. Reorder the terms: -70 + 8 + 14x + 7x2 = -8 + 8 Combine like terms: -70 + 8 = -62 -62 + 14x + 7x2 = -8 + 8 Combine like terms: -8 + 8 = 0 -62 + 14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -8.857142857 + 2x + x2 = 0 Move the constant term to the right: Add '8.857142857' to each side of the equation. -8.857142857 + 2x + 8.857142857 + x2 = 0 + 8.857142857 Reorder the terms: -8.857142857 + 8.857142857 + 2x + x2 = 0 + 8.857142857 Combine like terms: -8.857142857 + 8.857142857 = 0.000000000 0.000000000 + 2x + x2 = 0 + 8.857142857 2x + x2 = 0 + 8.857142857 Combine like terms: 0 + 8.857142857 = 8.857142857 2x + x2 = 8.857142857 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 8.857142857 + 1 Reorder the terms: 1 + 2x + x2 = 8.857142857 + 1 Combine like terms: 8.857142857 + 1 = 9.857142857 1 + 2x + x2 = 9.857142857 Factor a perfect square on the left side: (x + 1)(x + 1) = 9.857142857 Calculate the square root of the right side: 3.139608711 Break this problem into two subproblems by setting (x + 1) equal to 3.139608711 and -3.139608711.Subproblem 1
x + 1 = 3.139608711 Simplifying x + 1 = 3.139608711 Reorder the terms: 1 + x = 3.139608711 Solving 1 + x = 3.139608711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.139608711 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.139608711 + -1 x = 3.139608711 + -1 Combine like terms: 3.139608711 + -1 = 2.139608711 x = 2.139608711 Simplifying x = 2.139608711Subproblem 2
x + 1 = -3.139608711 Simplifying x + 1 = -3.139608711 Reorder the terms: 1 + x = -3.139608711 Solving 1 + x = -3.139608711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.139608711 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.139608711 + -1 x = -3.139608711 + -1 Combine like terms: -3.139608711 + -1 = -4.139608711 x = -4.139608711 Simplifying x = -4.139608711Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.139608711, -4.139608711}
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