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Simplifying x + 9 = 4x2 + -8x + 4 Reorder the terms: 9 + x = 4x2 + -8x + 4 Reorder the terms: 9 + x = 4 + -8x + 4x2 Solving 9 + x = 4 + -8x + 4x2 Solving for variable 'x'. Reorder the terms: 9 + -4 + x + 8x + -4x2 = 4 + -8x + 4x2 + -4 + 8x + -4x2 Combine like terms: 9 + -4 = 5 5 + x + 8x + -4x2 = 4 + -8x + 4x2 + -4 + 8x + -4x2 Combine like terms: x + 8x = 9x 5 + 9x + -4x2 = 4 + -8x + 4x2 + -4 + 8x + -4x2 Reorder the terms: 5 + 9x + -4x2 = 4 + -4 + -8x + 8x + 4x2 + -4x2 Combine like terms: 4 + -4 = 0 5 + 9x + -4x2 = 0 + -8x + 8x + 4x2 + -4x2 5 + 9x + -4x2 = -8x + 8x + 4x2 + -4x2 Combine like terms: -8x + 8x = 0 5 + 9x + -4x2 = 0 + 4x2 + -4x2 5 + 9x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 5 + 9x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + -2.25x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -2.25x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -2.25x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -2.25x + x2 = 0 + 1.25 -2.25x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -2.25x + x2 = 1.25 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 1.25 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 1.25 + 1.265625 Combine like terms: 1.25 + 1.265625 = 2.515625 1.265625 + -2.25x + x2 = 2.515625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (x + -1.125) equal to 1.586072193 and -1.586072193.Subproblem 1
x + -1.125 = 1.586072193 Simplifying x + -1.125 = 1.586072193 Reorder the terms: -1.125 + x = 1.586072193 Solving -1.125 + x = 1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.586072193 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.586072193 + 1.125 x = 1.586072193 + 1.125 Combine like terms: 1.586072193 + 1.125 = 2.711072193 x = 2.711072193 Simplifying x = 2.711072193Subproblem 2
x + -1.125 = -1.586072193 Simplifying x + -1.125 = -1.586072193 Reorder the terms: -1.125 + x = -1.586072193 Solving -1.125 + x = -1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.586072193 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.586072193 + 1.125 x = -1.586072193 + 1.125 Combine like terms: -1.586072193 + 1.125 = -0.461072193 x = -0.461072193 Simplifying x = -0.461072193Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.711072193, -0.461072193}
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