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Simplifying 0 = 16(x2) + -7x + -150 Reorder the terms: 0 = -150 + -7x + 16x2 Solving 0 = -150 + -7x + 16x2 Solving for variable 'x'. Combine like terms: 0 + 150 = 150 150 + 7x + -16x2 = -150 + -7x + 16x2 + 150 + 7x + -16x2 Reorder the terms: 150 + 7x + -16x2 = -150 + 150 + -7x + 7x + 16x2 + -16x2 Combine like terms: -150 + 150 = 0 150 + 7x + -16x2 = 0 + -7x + 7x + 16x2 + -16x2 150 + 7x + -16x2 = -7x + 7x + 16x2 + -16x2 Combine like terms: -7x + 7x = 0 150 + 7x + -16x2 = 0 + 16x2 + -16x2 150 + 7x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 150 + 7x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -9.375 + -0.4375x + x2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + -0.4375x + 9.375 + x2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + -0.4375x + x2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + -0.4375x + x2 = 0 + 9.375 -0.4375x + x2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 -0.4375x + x2 = 9.375 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 = 9.375 + 0.0478515625 Reorder the terms: 0.0478515625 + -0.4375x + x2 = 9.375 + 0.0478515625 Combine like terms: 9.375 + 0.0478515625 = 9.4228515625 0.0478515625 + -0.4375x + x2 = 9.4228515625 Factor a perfect square on the left side: (x + -0.21875)(x + -0.21875) = 9.4228515625 Calculate the square root of the right side: 3.06966636 Break this problem into two subproblems by setting (x + -0.21875) equal to 3.06966636 and -3.06966636.Subproblem 1
x + -0.21875 = 3.06966636 Simplifying x + -0.21875 = 3.06966636 Reorder the terms: -0.21875 + x = 3.06966636 Solving -0.21875 + x = 3.06966636 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 = 3.06966636 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + x = 3.06966636 + 0.21875 x = 3.06966636 + 0.21875 Combine like terms: 3.06966636 + 0.21875 = 3.28841636 x = 3.28841636 Simplifying x = 3.28841636Subproblem 2
x + -0.21875 = -3.06966636 Simplifying x + -0.21875 = -3.06966636 Reorder the terms: -0.21875 + x = -3.06966636 Solving -0.21875 + x = -3.06966636 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 = -3.06966636 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + x = -3.06966636 + 0.21875 x = -3.06966636 + 0.21875 Combine like terms: -3.06966636 + 0.21875 = -2.85091636 x = -2.85091636 Simplifying x = -2.85091636Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.28841636, -2.85091636}
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