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Simplifying 3x2 + -5x + 4 = 61 Reorder the terms: 4 + -5x + 3x2 = 61 Solving 4 + -5x + 3x2 = 61 Solving for variable 'x'. Reorder the terms: 4 + -61 + -5x + 3x2 = 61 + -61 Combine like terms: 4 + -61 = -57 -57 + -5x + 3x2 = 61 + -61 Combine like terms: 61 + -61 = 0 -57 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -19 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + -1.666666667x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -1.666666667x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -1.666666667x + x2 = 0 + 19 -1.666666667x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -1.666666667x + x2 = 19 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 19 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 19 + 0.6944444447 Combine like terms: 19 + 0.6944444447 = 19.6944444447 0.6944444447 + -1.666666667x + x2 = 19.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 19.6944444447 Calculate the square root of the right side: 4.437842319 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 4.437842319 and -4.437842319.Subproblem 1
x + -0.8333333335 = 4.437842319 Simplifying x + -0.8333333335 = 4.437842319 Reorder the terms: -0.8333333335 + x = 4.437842319 Solving -0.8333333335 + x = 4.437842319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 4.437842319 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 4.437842319 + 0.8333333335 x = 4.437842319 + 0.8333333335 Combine like terms: 4.437842319 + 0.8333333335 = 5.2711756525 x = 5.2711756525 Simplifying x = 5.2711756525Subproblem 2
x + -0.8333333335 = -4.437842319 Simplifying x + -0.8333333335 = -4.437842319 Reorder the terms: -0.8333333335 + x = -4.437842319 Solving -0.8333333335 + x = -4.437842319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -4.437842319 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -4.437842319 + 0.8333333335 x = -4.437842319 + 0.8333333335 Combine like terms: -4.437842319 + 0.8333333335 = -3.6045089855 x = -3.6045089855 Simplifying x = -3.6045089855Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.2711756525, -3.6045089855}
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