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Simplifying 0 = 4x2 + 95x + -30 Reorder the terms: 0 = -30 + 95x + 4x2 Solving 0 = -30 + 95x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 30 = 30 30 + -95x + -4x2 = -30 + 95x + 4x2 + 30 + -95x + -4x2 Reorder the terms: 30 + -95x + -4x2 = -30 + 30 + 95x + -95x + 4x2 + -4x2 Combine like terms: -30 + 30 = 0 30 + -95x + -4x2 = 0 + 95x + -95x + 4x2 + -4x2 30 + -95x + -4x2 = 95x + -95x + 4x2 + -4x2 Combine like terms: 95x + -95x = 0 30 + -95x + -4x2 = 0 + 4x2 + -4x2 30 + -95x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 30 + -95x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -7.5 + 23.75x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 23.75x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 23.75x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 23.75x + x2 = 0 + 7.5 23.75x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 23.75x + x2 = 7.5 The x term is 23.75x. Take half its coefficient (11.875). Square it (141.015625) and add it to both sides. Add '141.015625' to each side of the equation. 23.75x + 141.015625 + x2 = 7.5 + 141.015625 Reorder the terms: 141.015625 + 23.75x + x2 = 7.5 + 141.015625 Combine like terms: 7.5 + 141.015625 = 148.515625 141.015625 + 23.75x + x2 = 148.515625 Factor a perfect square on the left side: (x + 11.875)(x + 11.875) = 148.515625 Calculate the square root of the right side: 12.186698692 Break this problem into two subproblems by setting (x + 11.875) equal to 12.186698692 and -12.186698692.Subproblem 1
x + 11.875 = 12.186698692 Simplifying x + 11.875 = 12.186698692 Reorder the terms: 11.875 + x = 12.186698692 Solving 11.875 + x = 12.186698692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.875' to each side of the equation. 11.875 + -11.875 + x = 12.186698692 + -11.875 Combine like terms: 11.875 + -11.875 = 0.000 0.000 + x = 12.186698692 + -11.875 x = 12.186698692 + -11.875 Combine like terms: 12.186698692 + -11.875 = 0.311698692 x = 0.311698692 Simplifying x = 0.311698692Subproblem 2
x + 11.875 = -12.186698692 Simplifying x + 11.875 = -12.186698692 Reorder the terms: 11.875 + x = -12.186698692 Solving 11.875 + x = -12.186698692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.875' to each side of the equation. 11.875 + -11.875 + x = -12.186698692 + -11.875 Combine like terms: 11.875 + -11.875 = 0.000 0.000 + x = -12.186698692 + -11.875 x = -12.186698692 + -11.875 Combine like terms: -12.186698692 + -11.875 = -24.061698692 x = -24.061698692 Simplifying x = -24.061698692Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.311698692, -24.061698692}
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