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Simplifying -16x2 + 135x + 7 = 0 Reorder the terms: 7 + 135x + -16x2 = 0 Solving 7 + 135x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.4375 + -8.4375x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -8.4375x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -8.4375x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -8.4375x + x2 = 0 + 0.4375 -8.4375x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -8.4375x + x2 = 0.4375 The x term is -8.4375x. Take half its coefficient (-4.21875). Square it (17.79785156) and add it to both sides. Add '17.79785156' to each side of the equation. -8.4375x + 17.79785156 + x2 = 0.4375 + 17.79785156 Reorder the terms: 17.79785156 + -8.4375x + x2 = 0.4375 + 17.79785156 Combine like terms: 0.4375 + 17.79785156 = 18.23535156 17.79785156 + -8.4375x + x2 = 18.23535156 Factor a perfect square on the left side: (x + -4.21875)(x + -4.21875) = 18.23535156 Calculate the square root of the right side: 4.270287058 Break this problem into two subproblems by setting (x + -4.21875) equal to 4.270287058 and -4.270287058.Subproblem 1
x + -4.21875 = 4.270287058 Simplifying x + -4.21875 = 4.270287058 Reorder the terms: -4.21875 + x = 4.270287058 Solving -4.21875 + x = 4.270287058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.21875' to each side of the equation. -4.21875 + 4.21875 + x = 4.270287058 + 4.21875 Combine like terms: -4.21875 + 4.21875 = 0.00000 0.00000 + x = 4.270287058 + 4.21875 x = 4.270287058 + 4.21875 Combine like terms: 4.270287058 + 4.21875 = 8.489037058 x = 8.489037058 Simplifying x = 8.489037058Subproblem 2
x + -4.21875 = -4.270287058 Simplifying x + -4.21875 = -4.270287058 Reorder the terms: -4.21875 + x = -4.270287058 Solving -4.21875 + x = -4.270287058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.21875' to each side of the equation. -4.21875 + 4.21875 + x = -4.270287058 + 4.21875 Combine like terms: -4.21875 + 4.21875 = 0.00000 0.00000 + x = -4.270287058 + 4.21875 x = -4.270287058 + 4.21875 Combine like terms: -4.270287058 + 4.21875 = -0.051537058 x = -0.051537058 Simplifying x = -0.051537058Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.489037058, -0.051537058}
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