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Simplifying 25x2 + 9x + -80 = 0 Reorder the terms: -80 + 9x + 25x2 = 0 Solving -80 + 9x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -3.2 + 0.36x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 0.36x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 0.36x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 0.36x + x2 = 0 + 3.2 0.36x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 0.36x + x2 = 3.2 The x term is 0.36x. Take half its coefficient (0.18). Square it (0.0324) and add it to both sides. Add '0.0324' to each side of the equation. 0.36x + 0.0324 + x2 = 3.2 + 0.0324 Reorder the terms: 0.0324 + 0.36x + x2 = 3.2 + 0.0324 Combine like terms: 3.2 + 0.0324 = 3.2324 0.0324 + 0.36x + x2 = 3.2324 Factor a perfect square on the left side: (x + 0.18)(x + 0.18) = 3.2324 Calculate the square root of the right side: 1.797887649 Break this problem into two subproblems by setting (x + 0.18) equal to 1.797887649 and -1.797887649.Subproblem 1
x + 0.18 = 1.797887649 Simplifying x + 0.18 = 1.797887649 Reorder the terms: 0.18 + x = 1.797887649 Solving 0.18 + x = 1.797887649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.18' to each side of the equation. 0.18 + -0.18 + x = 1.797887649 + -0.18 Combine like terms: 0.18 + -0.18 = 0.00 0.00 + x = 1.797887649 + -0.18 x = 1.797887649 + -0.18 Combine like terms: 1.797887649 + -0.18 = 1.617887649 x = 1.617887649 Simplifying x = 1.617887649Subproblem 2
x + 0.18 = -1.797887649 Simplifying x + 0.18 = -1.797887649 Reorder the terms: 0.18 + x = -1.797887649 Solving 0.18 + x = -1.797887649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.18' to each side of the equation. 0.18 + -0.18 + x = -1.797887649 + -0.18 Combine like terms: 0.18 + -0.18 = 0.00 0.00 + x = -1.797887649 + -0.18 x = -1.797887649 + -0.18 Combine like terms: -1.797887649 + -0.18 = -1.977887649 x = -1.977887649 Simplifying x = -1.977887649Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.617887649, -1.977887649}
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