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Simplifying x2 + -24x = 2.2 Reorder the terms: -24x + x2 = 2.2 Solving -24x + x2 = 2.2 Solving for variable 'x'. Reorder the terms: -2.2 + -24x + x2 = 2.2 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 -2.2 + -24x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -24x + 2.2 + x2 = 0.0 + 2.2 Reorder the terms: -2.2 + 2.2 + -24x + x2 = 0.0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -24x + x2 = 0.0 + 2.2 -24x + x2 = 0.0 + 2.2 Combine like terms: 0.0 + 2.2 = 2.2 -24x + x2 = 2.2 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 = 2.2 + 144 Reorder the terms: 144 + -24x + x2 = 2.2 + 144 Combine like terms: 2.2 + 144 = 146.2 144 + -24x + x2 = 146.2 Factor a perfect square on the left side: (x + -12)(x + -12) = 146.2 Calculate the square root of the right side: 12.0913192 Break this problem into two subproblems by setting (x + -12) equal to 12.0913192 and -12.0913192.Subproblem 1
x + -12 = 12.0913192 Simplifying x + -12 = 12.0913192 Reorder the terms: -12 + x = 12.0913192 Solving -12 + x = 12.0913192 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 = 12.0913192 + 12 Combine like terms: -12 + 12 = 0 0 + x = 12.0913192 + 12 x = 12.0913192 + 12 Combine like terms: 12.0913192 + 12 = 24.0913192 x = 24.0913192 Simplifying x = 24.0913192Subproblem 2
x + -12 = -12.0913192 Simplifying x + -12 = -12.0913192 Reorder the terms: -12 + x = -12.0913192 Solving -12 + x = -12.0913192 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 = -12.0913192 + 12 Combine like terms: -12 + 12 = 0 0 + x = -12.0913192 + 12 x = -12.0913192 + 12 Combine like terms: -12.0913192 + 12 = -0.0913192 x = -0.0913192 Simplifying x = -0.0913192Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.0913192, -0.0913192}
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