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Simplifying 4x2 + 9x + -47 = 0 Reorder the terms: -47 + 9x + 4x2 = 0 Solving -47 + 9x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.75 + 2.25x + x2 = 0 Move the constant term to the right: Add '11.75' to each side of the equation. -11.75 + 2.25x + 11.75 + x2 = 0 + 11.75 Reorder the terms: -11.75 + 11.75 + 2.25x + x2 = 0 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + 2.25x + x2 = 0 + 11.75 2.25x + x2 = 0 + 11.75 Combine like terms: 0 + 11.75 = 11.75 2.25x + x2 = 11.75 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 11.75 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 11.75 + 1.265625 Combine like terms: 11.75 + 1.265625 = 13.015625 1.265625 + 2.25x + x2 = 13.015625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 13.015625 Calculate the square root of the right side: 3.607717422 Break this problem into two subproblems by setting (x + 1.125) equal to 3.607717422 and -3.607717422.Subproblem 1
x + 1.125 = 3.607717422 Simplifying x + 1.125 = 3.607717422 Reorder the terms: 1.125 + x = 3.607717422 Solving 1.125 + x = 3.607717422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 3.607717422 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 3.607717422 + -1.125 x = 3.607717422 + -1.125 Combine like terms: 3.607717422 + -1.125 = 2.482717422 x = 2.482717422 Simplifying x = 2.482717422Subproblem 2
x + 1.125 = -3.607717422 Simplifying x + 1.125 = -3.607717422 Reorder the terms: 1.125 + x = -3.607717422 Solving 1.125 + x = -3.607717422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -3.607717422 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -3.607717422 + -1.125 x = -3.607717422 + -1.125 Combine like terms: -3.607717422 + -1.125 = -4.732717422 x = -4.732717422 Simplifying x = -4.732717422Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.482717422, -4.732717422}
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