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Simplifying x2 + -5.2x = 42.24 Reorder the terms: -5.2x + x2 = 42.24 Solving -5.2x + x2 = 42.24 Solving for variable 'x'. Reorder the terms: -42.24 + -5.2x + x2 = 42.24 + -42.24 Combine like terms: 42.24 + -42.24 = 0.00 -42.24 + -5.2x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '42.24' to each side of the equation. -42.24 + -5.2x + 42.24 + x2 = 0.00 + 42.24 Reorder the terms: -42.24 + 42.24 + -5.2x + x2 = 0.00 + 42.24 Combine like terms: -42.24 + 42.24 = 0.00 0.00 + -5.2x + x2 = 0.00 + 42.24 -5.2x + x2 = 0.00 + 42.24 Combine like terms: 0.00 + 42.24 = 42.24 -5.2x + x2 = 42.24 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = 42.24 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = 42.24 + 6.76 Combine like terms: 42.24 + 6.76 = 49 6.76 + -5.2x + x2 = 49 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 49 Calculate the square root of the right side: 7 Break this problem into two subproblems by setting (x + -2.6) equal to 7 and -7.Subproblem 1
x + -2.6 = 7 Simplifying x + -2.6 = 7 Reorder the terms: -2.6 + x = 7 Solving -2.6 + x = 7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 7 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 7 + 2.6 x = 7 + 2.6 Combine like terms: 7 + 2.6 = 9.6 x = 9.6 Simplifying x = 9.6Subproblem 2
x + -2.6 = -7 Simplifying x + -2.6 = -7 Reorder the terms: -2.6 + x = -7 Solving -2.6 + x = -7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -7 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -7 + 2.6 x = -7 + 2.6 Combine like terms: -7 + 2.6 = -4.4 x = -4.4 Simplifying x = -4.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.6, -4.4}
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