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Simplifying 0 = -16x2 + 30x + 100 Reorder the terms: 0 = 100 + 30x + -16x2 Solving 0 = 100 + 30x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -100 = -100 -100 + -30x + 16x2 = 100 + 30x + -16x2 + -100 + -30x + 16x2 Reorder the terms: -100 + -30x + 16x2 = 100 + -100 + 30x + -30x + -16x2 + 16x2 Combine like terms: 100 + -100 = 0 -100 + -30x + 16x2 = 0 + 30x + -30x + -16x2 + 16x2 -100 + -30x + 16x2 = 30x + -30x + -16x2 + 16x2 Combine like terms: 30x + -30x = 0 -100 + -30x + 16x2 = 0 + -16x2 + 16x2 -100 + -30x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -100 + -30x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + -15x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + -15x + 8x2)' equal to zero and attempt to solve: Simplifying -50 + -15x + 8x2 = 0 Solving -50 + -15x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.25 + -1.875x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -1.875x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -1.875x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -1.875x + x2 = 0 + 6.25 -1.875x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -1.875x + x2 = 6.25 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 = 6.25 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = 6.25 + 0.87890625 Combine like terms: 6.25 + 0.87890625 = 7.12890625 0.87890625 + -1.875x + x2 = 7.12890625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 7.12890625 Calculate the square root of the right side: 2.67000117 Break this problem into two subproblems by setting (x + -0.9375) equal to 2.67000117 and -2.67000117.Subproblem 1
x + -0.9375 = 2.67000117 Simplifying x + -0.9375 = 2.67000117 Reorder the terms: -0.9375 + x = 2.67000117 Solving -0.9375 + x = 2.67000117 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 = 2.67000117 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 2.67000117 + 0.9375 x = 2.67000117 + 0.9375 Combine like terms: 2.67000117 + 0.9375 = 3.60750117 x = 3.60750117 Simplifying x = 3.60750117Subproblem 2
x + -0.9375 = -2.67000117 Simplifying x + -0.9375 = -2.67000117 Reorder the terms: -0.9375 + x = -2.67000117 Solving -0.9375 + x = -2.67000117 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 = -2.67000117 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -2.67000117 + 0.9375 x = -2.67000117 + 0.9375 Combine like terms: -2.67000117 + 0.9375 = -1.73250117 x = -1.73250117 Simplifying x = -1.73250117Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.60750117, -1.73250117}Solution
x = {3.60750117, -1.73250117}
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