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Simplifying 28x2 + 7x + -9 = 0 Reorder the terms: -9 + 7x + 28x2 = 0 Solving -9 + 7x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.3214285714 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.3214285714' to each side of the equation. -0.3214285714 + 0.25x + 0.3214285714 + x2 = 0 + 0.3214285714 Reorder the terms: -0.3214285714 + 0.3214285714 + 0.25x + x2 = 0 + 0.3214285714 Combine like terms: -0.3214285714 + 0.3214285714 = 0.0000000000 0.0000000000 + 0.25x + x2 = 0 + 0.3214285714 0.25x + x2 = 0 + 0.3214285714 Combine like terms: 0 + 0.3214285714 = 0.3214285714 0.25x + x2 = 0.3214285714 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 0.3214285714 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.3214285714 + 0.015625 Combine like terms: 0.3214285714 + 0.015625 = 0.3370535714 0.015625 + 0.25x + x2 = 0.3370535714 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.3370535714 Calculate the square root of the right side: 0.58056315 Break this problem into two subproblems by setting (x + 0.125) equal to 0.58056315 and -0.58056315.Subproblem 1
x + 0.125 = 0.58056315 Simplifying x + 0.125 = 0.58056315 Reorder the terms: 0.125 + x = 0.58056315 Solving 0.125 + x = 0.58056315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.58056315 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.58056315 + -0.125 x = 0.58056315 + -0.125 Combine like terms: 0.58056315 + -0.125 = 0.45556315 x = 0.45556315 Simplifying x = 0.45556315Subproblem 2
x + 0.125 = -0.58056315 Simplifying x + 0.125 = -0.58056315 Reorder the terms: 0.125 + x = -0.58056315 Solving 0.125 + x = -0.58056315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.58056315 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.58056315 + -0.125 x = -0.58056315 + -0.125 Combine like terms: -0.58056315 + -0.125 = -0.70556315 x = -0.70556315 Simplifying x = -0.70556315Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.45556315, -0.70556315}
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