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Simplifying 17.5 = 16x(x + 2) Reorder the terms: 17.5 = 16x(2 + x) 17.5 = (2 * 16x + x * 16x) 17.5 = (32x + 16x2) Solving 17.5 = 32x + 16x2 Solving for variable 'x'. Reorder the terms: 17.5 + -32x + -16x2 = 32x + -32x + 16x2 + -16x2 Combine like terms: 32x + -32x = 0 17.5 + -32x + -16x2 = 0 + 16x2 + -16x2 17.5 + -32x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 17.5 + -32x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -1.09375 + 2x + x2 = 0 Move the constant term to the right: Add '1.09375' to each side of the equation. -1.09375 + 2x + 1.09375 + x2 = 0 + 1.09375 Reorder the terms: -1.09375 + 1.09375 + 2x + x2 = 0 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + 2x + x2 = 0 + 1.09375 2x + x2 = 0 + 1.09375 Combine like terms: 0 + 1.09375 = 1.09375 2x + x2 = 1.09375 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1.09375 + 1 Reorder the terms: 1 + 2x + x2 = 1.09375 + 1 Combine like terms: 1.09375 + 1 = 2.09375 1 + 2x + x2 = 2.09375 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.09375 Calculate the square root of the right side: 1.446979613 Break this problem into two subproblems by setting (x + 1) equal to 1.446979613 and -1.446979613.Subproblem 1
x + 1 = 1.446979613 Simplifying x + 1 = 1.446979613 Reorder the terms: 1 + x = 1.446979613 Solving 1 + x = 1.446979613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.446979613 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.446979613 + -1 x = 1.446979613 + -1 Combine like terms: 1.446979613 + -1 = 0.446979613 x = 0.446979613 Simplifying x = 0.446979613Subproblem 2
x + 1 = -1.446979613 Simplifying x + 1 = -1.446979613 Reorder the terms: 1 + x = -1.446979613 Solving 1 + x = -1.446979613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.446979613 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.446979613 + -1 x = -1.446979613 + -1 Combine like terms: -1.446979613 + -1 = -2.446979613 x = -2.446979613 Simplifying x = -2.446979613Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.446979613, -2.446979613}
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