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Simplifying 710x2 + -390.5x + 17.75 = 0 Reorder the terms: 17.75 + -390.5x + 710x2 = 0 Solving 17.75 + -390.5x + 710x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 710 the coefficient of the squared term: Divide each side by '710'. 0.025 + -0.55x + x2 = 0 Move the constant term to the right: Add '-0.025' to each side of the equation. 0.025 + -0.55x + -0.025 + x2 = 0 + -0.025 Reorder the terms: 0.025 + -0.025 + -0.55x + x2 = 0 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + -0.55x + x2 = 0 + -0.025 -0.55x + x2 = 0 + -0.025 Combine like terms: 0 + -0.025 = -0.025 -0.55x + x2 = -0.025 The x term is -0.55x. Take half its coefficient (-0.275). Square it (0.075625) and add it to both sides. Add '0.075625' to each side of the equation. -0.55x + 0.075625 + x2 = -0.025 + 0.075625 Reorder the terms: 0.075625 + -0.55x + x2 = -0.025 + 0.075625 Combine like terms: -0.025 + 0.075625 = 0.050625 0.075625 + -0.55x + x2 = 0.050625 Factor a perfect square on the left side: (x + -0.275)(x + -0.275) = 0.050625 Calculate the square root of the right side: 0.225 Break this problem into two subproblems by setting (x + -0.275) equal to 0.225 and -0.225.Subproblem 1
x + -0.275 = 0.225 Simplifying x + -0.275 = 0.225 Reorder the terms: -0.275 + x = 0.225 Solving -0.275 + x = 0.225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + x = 0.225 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + x = 0.225 + 0.275 x = 0.225 + 0.275 Combine like terms: 0.225 + 0.275 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + -0.275 = -0.225 Simplifying x + -0.275 = -0.225 Reorder the terms: -0.275 + x = -0.225 Solving -0.275 + x = -0.225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + x = -0.225 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + x = -0.225 + 0.275 x = -0.225 + 0.275 Combine like terms: -0.225 + 0.275 = 0.05 x = 0.05 Simplifying x = 0.05Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, 0.05}
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