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Simplifying -16x2 + -30x + 350 = 0 Reorder the terms: 350 + -30x + -16x2 = 0 Solving 350 + -30x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(175 + -15x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(175 + -15x + -8x2)' equal to zero and attempt to solve: Simplifying 175 + -15x + -8x2 = 0 Solving 175 + -15x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -21.875 + 1.875x + x2 = 0 Move the constant term to the right: Add '21.875' to each side of the equation. -21.875 + 1.875x + 21.875 + x2 = 0 + 21.875 Reorder the terms: -21.875 + 21.875 + 1.875x + x2 = 0 + 21.875 Combine like terms: -21.875 + 21.875 = 0.000 0.000 + 1.875x + x2 = 0 + 21.875 1.875x + x2 = 0 + 21.875 Combine like terms: 0 + 21.875 = 21.875 1.875x + x2 = 21.875 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 = 21.875 + 0.87890625 Reorder the terms: 0.87890625 + 1.875x + x2 = 21.875 + 0.87890625 Combine like terms: 21.875 + 0.87890625 = 22.75390625 0.87890625 + 1.875x + x2 = 22.75390625 Factor a perfect square on the left side: (x + 0.9375)(x + 0.9375) = 22.75390625 Calculate the square root of the right side: 4.770105476 Break this problem into two subproblems by setting (x + 0.9375) equal to 4.770105476 and -4.770105476.Subproblem 1
x + 0.9375 = 4.770105476 Simplifying x + 0.9375 = 4.770105476 Reorder the terms: 0.9375 + x = 4.770105476 Solving 0.9375 + x = 4.770105476 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 = 4.770105476 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = 4.770105476 + -0.9375 x = 4.770105476 + -0.9375 Combine like terms: 4.770105476 + -0.9375 = 3.832605476 x = 3.832605476 Simplifying x = 3.832605476Subproblem 2
x + 0.9375 = -4.770105476 Simplifying x + 0.9375 = -4.770105476 Reorder the terms: 0.9375 + x = -4.770105476 Solving 0.9375 + x = -4.770105476 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 = -4.770105476 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = -4.770105476 + -0.9375 x = -4.770105476 + -0.9375 Combine like terms: -4.770105476 + -0.9375 = -5.707605476 x = -5.707605476 Simplifying x = -5.707605476Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.832605476, -5.707605476}Solution
x = {3.832605476, -5.707605476}
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