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Simplifying 7x2 + 12x + -7 = 0 Reorder the terms: -7 + 12x + 7x2 = 0 Solving -7 + 12x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.714285714x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.714285714x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.714285714x + x2 = 0 + 1 1.714285714x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.714285714x + x2 = 1 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 = 1 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = 1 + 0.7346938773 Combine like terms: 1 + 0.7346938773 = 1.7346938773 0.7346938773 + 1.714285714x + x2 = 1.7346938773 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = 1.7346938773 Calculate the square root of the right side: 1.31707778 Break this problem into two subproblems by setting (x + 0.857142857) equal to 1.31707778 and -1.31707778.Subproblem 1
x + 0.857142857 = 1.31707778 Simplifying x + 0.857142857 = 1.31707778 Reorder the terms: 0.857142857 + x = 1.31707778 Solving 0.857142857 + x = 1.31707778 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 = 1.31707778 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = 1.31707778 + -0.857142857 x = 1.31707778 + -0.857142857 Combine like terms: 1.31707778 + -0.857142857 = 0.459934923 x = 0.459934923 Simplifying x = 0.459934923Subproblem 2
x + 0.857142857 = -1.31707778 Simplifying x + 0.857142857 = -1.31707778 Reorder the terms: 0.857142857 + x = -1.31707778 Solving 0.857142857 + x = -1.31707778 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 = -1.31707778 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = -1.31707778 + -0.857142857 x = -1.31707778 + -0.857142857 Combine like terms: -1.31707778 + -0.857142857 = -2.174220637 x = -2.174220637 Simplifying x = -2.174220637Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.459934923, -2.174220637}
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