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Simplifying x2 + 24x = 10 Reorder the terms: 24x + x2 = 10 Solving 24x + x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 24x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 24x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 24x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 24x + x2 = 0 + 10 24x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 24x + x2 = 10 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 = 10 + 144 Reorder the terms: 144 + 24x + x2 = 10 + 144 Combine like terms: 10 + 144 = 154 144 + 24x + x2 = 154 Factor a perfect square on the left side: (x + 12)(x + 12) = 154 Calculate the square root of the right side: 12.409673646 Break this problem into two subproblems by setting (x + 12) equal to 12.409673646 and -12.409673646.Subproblem 1
x + 12 = 12.409673646 Simplifying x + 12 = 12.409673646 Reorder the terms: 12 + x = 12.409673646 Solving 12 + x = 12.409673646 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 = 12.409673646 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.409673646 + -12 x = 12.409673646 + -12 Combine like terms: 12.409673646 + -12 = 0.409673646 x = 0.409673646 Simplifying x = 0.409673646Subproblem 2
x + 12 = -12.409673646 Simplifying x + 12 = -12.409673646 Reorder the terms: 12 + x = -12.409673646 Solving 12 + x = -12.409673646 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 = -12.409673646 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.409673646 + -12 x = -12.409673646 + -12 Combine like terms: -12.409673646 + -12 = -24.409673646 x = -24.409673646 Simplifying x = -24.409673646Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.409673646, -24.409673646}
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