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Simplifying 0 = -16x2 + 30x + 160 Reorder the terms: 0 = 160 + 30x + -16x2 Solving 0 = 160 + 30x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -160 = -160 -160 + -30x + 16x2 = 160 + 30x + -16x2 + -160 + -30x + 16x2 Reorder the terms: -160 + -30x + 16x2 = 160 + -160 + 30x + -30x + -16x2 + 16x2 Combine like terms: 160 + -160 = 0 -160 + -30x + 16x2 = 0 + 30x + -30x + -16x2 + 16x2 -160 + -30x + 16x2 = 30x + -30x + -16x2 + 16x2 Combine like terms: 30x + -30x = 0 -160 + -30x + 16x2 = 0 + -16x2 + 16x2 -160 + -30x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -160 + -30x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-80 + -15x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-80 + -15x + 8x2)' equal to zero and attempt to solve: Simplifying -80 + -15x + 8x2 = 0 Solving -80 + -15x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -10 + -1.875x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -1.875x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -1.875x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1.875x + x2 = 0 + 10 -1.875x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -1.875x + x2 = 10 The x term is -1.875x. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875x + 0.87890625 + x2 = 10 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = 10 + 0.87890625 Combine like terms: 10 + 0.87890625 = 10.87890625 0.87890625 + -1.875x + x2 = 10.87890625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 10.87890625 Calculate the square root of the right side: 3.2983187 Break this problem into two subproblems by setting (x + -0.9375) equal to 3.2983187 and -3.2983187.Subproblem 1
x + -0.9375 = 3.2983187 Simplifying x + -0.9375 = 3.2983187 Reorder the terms: -0.9375 + x = 3.2983187 Solving -0.9375 + x = 3.2983187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = 3.2983187 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 3.2983187 + 0.9375 x = 3.2983187 + 0.9375 Combine like terms: 3.2983187 + 0.9375 = 4.2358187 x = 4.2358187 Simplifying x = 4.2358187Subproblem 2
x + -0.9375 = -3.2983187 Simplifying x + -0.9375 = -3.2983187 Reorder the terms: -0.9375 + x = -3.2983187 Solving -0.9375 + x = -3.2983187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = -3.2983187 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -3.2983187 + 0.9375 x = -3.2983187 + 0.9375 Combine like terms: -3.2983187 + 0.9375 = -2.3608187 x = -2.3608187 Simplifying x = -2.3608187Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.2358187, -2.3608187}Solution
x = {4.2358187, -2.3608187}
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