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Simplifying 4x2 + -64x + -69 = 0 Reorder the terms: -69 + -64x + 4x2 = 0 Solving -69 + -64x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -17.25 + -16x + x2 = 0 Move the constant term to the right: Add '17.25' to each side of the equation. -17.25 + -16x + 17.25 + x2 = 0 + 17.25 Reorder the terms: -17.25 + 17.25 + -16x + x2 = 0 + 17.25 Combine like terms: -17.25 + 17.25 = 0.00 0.00 + -16x + x2 = 0 + 17.25 -16x + x2 = 0 + 17.25 Combine like terms: 0 + 17.25 = 17.25 -16x + x2 = 17.25 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 17.25 + 64 Reorder the terms: 64 + -16x + x2 = 17.25 + 64 Combine like terms: 17.25 + 64 = 81.25 64 + -16x + x2 = 81.25 Factor a perfect square on the left side: (x + -8)(x + -8) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + -8) equal to 9.013878189 and -9.013878189.Subproblem 1
x + -8 = 9.013878189 Simplifying x + -8 = 9.013878189 Reorder the terms: -8 + x = 9.013878189 Solving -8 + x = 9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 9.013878189 + 8 Combine like terms: -8 + 8 = 0 0 + x = 9.013878189 + 8 x = 9.013878189 + 8 Combine like terms: 9.013878189 + 8 = 17.013878189 x = 17.013878189 Simplifying x = 17.013878189Subproblem 2
x + -8 = -9.013878189 Simplifying x + -8 = -9.013878189 Reorder the terms: -8 + x = -9.013878189 Solving -8 + x = -9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -9.013878189 + 8 Combine like terms: -8 + 8 = 0 0 + x = -9.013878189 + 8 x = -9.013878189 + 8 Combine like terms: -9.013878189 + 8 = -1.013878189 x = -1.013878189 Simplifying x = -1.013878189Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.013878189, -1.013878189}
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