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Simplifying 8x2 + 14x + -7 = 0 Reorder the terms: -7 + 14x + 8x2 = 0 Solving -7 + 14x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + 1.75x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 1.75x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 1.75x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 1.75x + x2 = 0 + 0.875 1.75x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 1.75x + x2 = 0.875 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 0.875 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 0.875 + 0.765625 Combine like terms: 0.875 + 0.765625 = 1.640625 0.765625 + 1.75x + x2 = 1.640625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (x + 0.875) equal to 1.280868846 and -1.280868846.Subproblem 1
x + 0.875 = 1.280868846 Simplifying x + 0.875 = 1.280868846 Reorder the terms: 0.875 + x = 1.280868846 Solving 0.875 + x = 1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.280868846 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.280868846 + -0.875 x = 1.280868846 + -0.875 Combine like terms: 1.280868846 + -0.875 = 0.405868846 x = 0.405868846 Simplifying x = 0.405868846Subproblem 2
x + 0.875 = -1.280868846 Simplifying x + 0.875 = -1.280868846 Reorder the terms: 0.875 + x = -1.280868846 Solving 0.875 + x = -1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.280868846 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.280868846 + -0.875 x = -1.280868846 + -0.875 Combine like terms: -1.280868846 + -0.875 = -2.155868846 x = -2.155868846 Simplifying x = -2.155868846Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.405868846, -2.155868846}
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