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Simplifying 28x2 + -7x + -16 = 0 Reorder the terms: -16 + -7x + 28x2 = 0 Solving -16 + -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'. -0.5714285714 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -0.25x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -0.25x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -0.25x + x2 = 0 + 0.5714285714 -0.25x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -0.25x + x2 = 0.5714285714 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 = 0.5714285714 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.5714285714 + 0.015625 Combine like terms: 0.5714285714 + 0.015625 = 0.5870535714 0.015625 + -0.25x + x2 = 0.5870535714 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.5870535714 Calculate the square root of the right side: 0.766194213 Break this problem into two subproblems by setting (x + -0.125) equal to 0.766194213 and -0.766194213.Subproblem 1
x + -0.125 = 0.766194213 Simplifying x + -0.125 = 0.766194213 Reorder the terms: -0.125 + x = 0.766194213 Solving -0.125 + x = 0.766194213 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 = 0.766194213 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.766194213 + 0.125 x = 0.766194213 + 0.125 Combine like terms: 0.766194213 + 0.125 = 0.891194213 x = 0.891194213 Simplifying x = 0.891194213Subproblem 2
x + -0.125 = -0.766194213 Simplifying x + -0.125 = -0.766194213 Reorder the terms: -0.125 + x = -0.766194213 Solving -0.125 + x = -0.766194213 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 = -0.766194213 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.766194213 + 0.125 x = -0.766194213 + 0.125 Combine like terms: -0.766194213 + 0.125 = -0.641194213 x = -0.641194213 Simplifying x = -0.641194213Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.891194213, -0.641194213}
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