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Simplifying x2 + 5.2x + -17.25 = 0 Reorder the terms: -17.25 + 5.2x + x2 = 0 Solving -17.25 + 5.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '17.25' to each side of the equation. -17.25 + 5.2x + 17.25 + x2 = 0 + 17.25 Reorder the terms: -17.25 + 17.25 + 5.2x + x2 = 0 + 17.25 Combine like terms: -17.25 + 17.25 = 0.00 0.00 + 5.2x + x2 = 0 + 17.25 5.2x + x2 = 0 + 17.25 Combine like terms: 0 + 17.25 = 17.25 5.2x + x2 = 17.25 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 = 17.25 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = 17.25 + 6.76 Combine like terms: 17.25 + 6.76 = 24.01 6.76 + 5.2x + x2 = 24.01 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 24.01 Calculate the square root of the right side: 4.9 Break this problem into two subproblems by setting (x + 2.6) equal to 4.9 and -4.9.Subproblem 1
x + 2.6 = 4.9 Simplifying x + 2.6 = 4.9 Reorder the terms: 2.6 + x = 4.9 Solving 2.6 + x = 4.9 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 = 4.9 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 4.9 + -2.6 x = 4.9 + -2.6 Combine like terms: 4.9 + -2.6 = 2.3 x = 2.3 Simplifying x = 2.3Subproblem 2
x + 2.6 = -4.9 Simplifying x + 2.6 = -4.9 Reorder the terms: 2.6 + x = -4.9 Solving 2.6 + x = -4.9 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 = -4.9 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -4.9 + -2.6 x = -4.9 + -2.6 Combine like terms: -4.9 + -2.6 = -7.5 x = -7.5 Simplifying x = -7.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3, -7.5}
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