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Simplifying 28x2 + -51x + -26 = 0 Reorder the terms: -26 + -51x + 28x2 = 0 Solving -26 + -51x + 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'. -0.9285714286 + -1.821428571x + x2 = 0 Move the constant term to the right: Add '0.9285714286' to each side of the equation. -0.9285714286 + -1.821428571x + 0.9285714286 + x2 = 0 + 0.9285714286 Reorder the terms: -0.9285714286 + 0.9285714286 + -1.821428571x + x2 = 0 + 0.9285714286 Combine like terms: -0.9285714286 + 0.9285714286 = 0.0000000000 0.0000000000 + -1.821428571x + x2 = 0 + 0.9285714286 -1.821428571x + x2 = 0 + 0.9285714286 Combine like terms: 0 + 0.9285714286 = 0.9285714286 -1.821428571x + x2 = 0.9285714286 The x term is -1.821428571x. Take half its coefficient (-0.9107142855). Square it (0.8294005098) and add it to both sides. Add '0.8294005098' to each side of the equation. -1.821428571x + 0.8294005098 + x2 = 0.9285714286 + 0.8294005098 Reorder the terms: 0.8294005098 + -1.821428571x + x2 = 0.9285714286 + 0.8294005098 Combine like terms: 0.9285714286 + 0.8294005098 = 1.7579719384 0.8294005098 + -1.821428571x + x2 = 1.7579719384 Factor a perfect square on the left side: (x + -0.9107142855)(x + -0.9107142855) = 1.7579719384 Calculate the square root of the right side: 1.325885341 Break this problem into two subproblems by setting (x + -0.9107142855) equal to 1.325885341 and -1.325885341.Subproblem 1
x + -0.9107142855 = 1.325885341 Simplifying x + -0.9107142855 = 1.325885341 Reorder the terms: -0.9107142855 + x = 1.325885341 Solving -0.9107142855 + x = 1.325885341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9107142855' to each side of the equation. -0.9107142855 + 0.9107142855 + x = 1.325885341 + 0.9107142855 Combine like terms: -0.9107142855 + 0.9107142855 = 0.0000000000 0.0000000000 + x = 1.325885341 + 0.9107142855 x = 1.325885341 + 0.9107142855 Combine like terms: 1.325885341 + 0.9107142855 = 2.2365996265 x = 2.2365996265 Simplifying x = 2.2365996265Subproblem 2
x + -0.9107142855 = -1.325885341 Simplifying x + -0.9107142855 = -1.325885341 Reorder the terms: -0.9107142855 + x = -1.325885341 Solving -0.9107142855 + x = -1.325885341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9107142855' to each side of the equation. -0.9107142855 + 0.9107142855 + x = -1.325885341 + 0.9107142855 Combine like terms: -0.9107142855 + 0.9107142855 = 0.0000000000 0.0000000000 + x = -1.325885341 + 0.9107142855 x = -1.325885341 + 0.9107142855 Combine like terms: -1.325885341 + 0.9107142855 = -0.4151710555 x = -0.4151710555 Simplifying x = -0.4151710555Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2365996265, -0.4151710555}
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