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Simplifying 256 = x2 + 2 * 3.5x + 12.25 + x2 Multiply 2 * 3.5 256 = x2 + 7x + 12.25 + x2 Reorder the terms: 256 = 12.25 + 7x + x2 + x2 Combine like terms: x2 + x2 = 2x2 256 = 12.25 + 7x + 2x2 Solving 256 = 12.25 + 7x + 2x2 Solving for variable 'x'. Combine like terms: 256 + -12.25 = 243.75 243.75 + -7x + -2x2 = 12.25 + 7x + 2x2 + -12.25 + -7x + -2x2 Reorder the terms: 243.75 + -7x + -2x2 = 12.25 + -12.25 + 7x + -7x + 2x2 + -2x2 Combine like terms: 12.25 + -12.25 = 0.00 243.75 + -7x + -2x2 = 0.00 + 7x + -7x + 2x2 + -2x2 243.75 + -7x + -2x2 = 7x + -7x + 2x2 + -2x2 Combine like terms: 7x + -7x = 0 243.75 + -7x + -2x2 = 0 + 2x2 + -2x2 243.75 + -7x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 243.75 + -7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -121.875 + 3.5x + x2 = 0 Move the constant term to the right: Add '121.875' to each side of the equation. -121.875 + 3.5x + 121.875 + x2 = 0 + 121.875 Reorder the terms: -121.875 + 121.875 + 3.5x + x2 = 0 + 121.875 Combine like terms: -121.875 + 121.875 = 0.000 0.000 + 3.5x + x2 = 0 + 121.875 3.5x + x2 = 0 + 121.875 Combine like terms: 0 + 121.875 = 121.875 3.5x + x2 = 121.875 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 121.875 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 121.875 + 3.0625 Combine like terms: 121.875 + 3.0625 = 124.9375 3.0625 + 3.5x + x2 = 124.9375 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 124.9375 Calculate the square root of the right side: 11.177544453 Break this problem into two subproblems by setting (x + 1.75) equal to 11.177544453 and -11.177544453.Subproblem 1
x + 1.75 = 11.177544453 Simplifying x + 1.75 = 11.177544453 Reorder the terms: 1.75 + x = 11.177544453 Solving 1.75 + x = 11.177544453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 11.177544453 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 11.177544453 + -1.75 x = 11.177544453 + -1.75 Combine like terms: 11.177544453 + -1.75 = 9.427544453 x = 9.427544453 Simplifying x = 9.427544453Subproblem 2
x + 1.75 = -11.177544453 Simplifying x + 1.75 = -11.177544453 Reorder the terms: 1.75 + x = -11.177544453 Solving 1.75 + x = -11.177544453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -11.177544453 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -11.177544453 + -1.75 x = -11.177544453 + -1.75 Combine like terms: -11.177544453 + -1.75 = -12.927544453 x = -12.927544453 Simplifying x = -12.927544453Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.427544453, -12.927544453}
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