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Simplifying 0 = 180 + 7x + -16x2 Solving 0 = 180 + 7x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -180 = -180 -180 + -7x + 16x2 = 180 + 7x + -16x2 + -180 + -7x + 16x2 Reorder the terms: -180 + -7x + 16x2 = 180 + -180 + 7x + -7x + -16x2 + 16x2 Combine like terms: 180 + -180 = 0 -180 + -7x + 16x2 = 0 + 7x + -7x + -16x2 + 16x2 -180 + -7x + 16x2 = 7x + -7x + -16x2 + 16x2 Combine like terms: 7x + -7x = 0 -180 + -7x + 16x2 = 0 + -16x2 + 16x2 -180 + -7x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -180 + -7x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -11.25 + -0.4375x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -0.4375x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -0.4375x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -0.4375x + x2 = 0 + 11.25 -0.4375x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -0.4375x + x2 = 11.25 The x term is -0.4375x. Take half its coefficient (-0.21875). Square it (0.0478515625) and add it to both sides. Add '0.0478515625' to each side of the equation. -0.4375x + 0.0478515625 + x2 = 11.25 + 0.0478515625 Reorder the terms: 0.0478515625 + -0.4375x + x2 = 11.25 + 0.0478515625 Combine like terms: 11.25 + 0.0478515625 = 11.2978515625 0.0478515625 + -0.4375x + x2 = 11.2978515625 Factor a perfect square on the left side: (x + -0.21875)(x + -0.21875) = 11.2978515625 Calculate the square root of the right side: 3.361227687 Break this problem into two subproblems by setting (x + -0.21875) equal to 3.361227687 and -3.361227687.Subproblem 1
x + -0.21875 = 3.361227687 Simplifying x + -0.21875 = 3.361227687 Reorder the terms: -0.21875 + x = 3.361227687 Solving -0.21875 + x = 3.361227687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.21875' to each side of the equation. -0.21875 + 0.21875 + x = 3.361227687 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + x = 3.361227687 + 0.21875 x = 3.361227687 + 0.21875 Combine like terms: 3.361227687 + 0.21875 = 3.579977687 x = 3.579977687 Simplifying x = 3.579977687Subproblem 2
x + -0.21875 = -3.361227687 Simplifying x + -0.21875 = -3.361227687 Reorder the terms: -0.21875 + x = -3.361227687 Solving -0.21875 + x = -3.361227687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.21875' to each side of the equation. -0.21875 + 0.21875 + x = -3.361227687 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + x = -3.361227687 + 0.21875 x = -3.361227687 + 0.21875 Combine like terms: -3.361227687 + 0.21875 = -3.142477687 x = -3.142477687 Simplifying x = -3.142477687Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.579977687, -3.142477687}
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