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Simplifying 4x2 + -5x + -11 = 144 Reorder the terms: -11 + -5x + 4x2 = 144 Solving -11 + -5x + 4x2 = 144 Solving for variable 'x'. Reorder the terms: -11 + -144 + -5x + 4x2 = 144 + -144 Combine like terms: -11 + -144 = -155 -155 + -5x + 4x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -155 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -38.75 + -1.25x + x2 = 0 Move the constant term to the right: Add '38.75' to each side of the equation. -38.75 + -1.25x + 38.75 + x2 = 0 + 38.75 Reorder the terms: -38.75 + 38.75 + -1.25x + x2 = 0 + 38.75 Combine like terms: -38.75 + 38.75 = 0.00 0.00 + -1.25x + x2 = 0 + 38.75 -1.25x + x2 = 0 + 38.75 Combine like terms: 0 + 38.75 = 38.75 -1.25x + x2 = 38.75 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 38.75 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 38.75 + 0.390625 Combine like terms: 38.75 + 0.390625 = 39.140625 0.390625 + -1.25x + x2 = 39.140625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 39.140625 Calculate the square root of the right side: 6.256246878 Break this problem into two subproblems by setting (x + -0.625) equal to 6.256246878 and -6.256246878.Subproblem 1
x + -0.625 = 6.256246878 Simplifying x + -0.625 = 6.256246878 Reorder the terms: -0.625 + x = 6.256246878 Solving -0.625 + x = 6.256246878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 6.256246878 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 6.256246878 + 0.625 x = 6.256246878 + 0.625 Combine like terms: 6.256246878 + 0.625 = 6.881246878 x = 6.881246878 Simplifying x = 6.881246878Subproblem 2
x + -0.625 = -6.256246878 Simplifying x + -0.625 = -6.256246878 Reorder the terms: -0.625 + x = -6.256246878 Solving -0.625 + x = -6.256246878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -6.256246878 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -6.256246878 + 0.625 x = -6.256246878 + 0.625 Combine like terms: -6.256246878 + 0.625 = -5.631246878 x = -5.631246878 Simplifying x = -5.631246878Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.881246878, -5.631246878}
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