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Simplifying -1x2 + 24x + 11 = 0 Reorder the terms: 11 + 24x + -1x2 = 0 Solving 11 + 24x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -24x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -24x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -24x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -24x + x2 = 0 + 11 -24x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -24x + x2 = 11 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 11 + 144 Reorder the terms: 144 + -24x + x2 = 11 + 144 Combine like terms: 11 + 144 = 155 144 + -24x + x2 = 155 Factor a perfect square on the left side: (x + -12)(x + -12) = 155 Calculate the square root of the right side: 12.449899598 Break this problem into two subproblems by setting (x + -12) equal to 12.449899598 and -12.449899598.Subproblem 1
x + -12 = 12.449899598 Simplifying x + -12 = 12.449899598 Reorder the terms: -12 + x = 12.449899598 Solving -12 + x = 12.449899598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 12.449899598 + 12 Combine like terms: -12 + 12 = 0 0 + x = 12.449899598 + 12 x = 12.449899598 + 12 Combine like terms: 12.449899598 + 12 = 24.449899598 x = 24.449899598 Simplifying x = 24.449899598Subproblem 2
x + -12 = -12.449899598 Simplifying x + -12 = -12.449899598 Reorder the terms: -12 + x = -12.449899598 Solving -12 + x = -12.449899598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -12.449899598 + 12 Combine like terms: -12 + 12 = 0 0 + x = -12.449899598 + 12 x = -12.449899598 + 12 Combine like terms: -12.449899598 + 12 = -0.449899598 x = -0.449899598 Simplifying x = -0.449899598Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.449899598, -0.449899598}
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