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Simplifying 40x2 + 5x + -28 = 0 Reorder the terms: -28 + 5x + 40x2 = 0 Solving -28 + 5x + 40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.7 + 0.125x + x2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + 0.125x + 0.7 + x2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + 0.125x + x2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + 0.125x + x2 = 0 + 0.7 0.125x + x2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 0.125x + x2 = 0.7 The x term is 0.125x. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125x + 0.00390625 + x2 = 0.7 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 0.7 + 0.00390625 Combine like terms: 0.7 + 0.00390625 = 0.70390625 0.00390625 + 0.125x + x2 = 0.70390625 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 0.70390625 Calculate the square root of the right side: 0.83899121 Break this problem into two subproblems by setting (x + 0.0625) equal to 0.83899121 and -0.83899121.Subproblem 1
x + 0.0625 = 0.83899121 Simplifying x + 0.0625 = 0.83899121 Reorder the terms: 0.0625 + x = 0.83899121 Solving 0.0625 + x = 0.83899121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = 0.83899121 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 0.83899121 + -0.0625 x = 0.83899121 + -0.0625 Combine like terms: 0.83899121 + -0.0625 = 0.77649121 x = 0.77649121 Simplifying x = 0.77649121Subproblem 2
x + 0.0625 = -0.83899121 Simplifying x + 0.0625 = -0.83899121 Reorder the terms: 0.0625 + x = -0.83899121 Solving 0.0625 + x = -0.83899121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = -0.83899121 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -0.83899121 + -0.0625 x = -0.83899121 + -0.0625 Combine like terms: -0.83899121 + -0.0625 = -0.90149121 x = -0.90149121 Simplifying x = -0.90149121Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.77649121, -0.90149121}
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