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Simplifying 4x + -3(16x2 + -24x + 9) = 0 Reorder the terms: 4x + -3(9 + -24x + 16x2) = 0 4x + (9 * -3 + -24x * -3 + 16x2 * -3) = 0 4x + (-27 + 72x + -48x2) = 0 Reorder the terms: -27 + 4x + 72x + -48x2 = 0 Combine like terms: 4x + 72x = 76x -27 + 76x + -48x2 = 0 Solving -27 + 76x + -48x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -48 the coefficient of the squared term: Divide each side by '-48'. 0.5625 + -1.583333333x + x2 = 0 Move the constant term to the right: Add '-0.5625' to each side of the equation. 0.5625 + -1.583333333x + -0.5625 + x2 = 0 + -0.5625 Reorder the terms: 0.5625 + -0.5625 + -1.583333333x + x2 = 0 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + -1.583333333x + x2 = 0 + -0.5625 -1.583333333x + x2 = 0 + -0.5625 Combine like terms: 0 + -0.5625 = -0.5625 -1.583333333x + x2 = -0.5625 The x term is -1.583333333x. Take half its coefficient (-0.7916666665). Square it (0.6267361108) and add it to both sides. Add '0.6267361108' to each side of the equation. -1.583333333x + 0.6267361108 + x2 = -0.5625 + 0.6267361108 Reorder the terms: 0.6267361108 + -1.583333333x + x2 = -0.5625 + 0.6267361108 Combine like terms: -0.5625 + 0.6267361108 = 0.0642361108 0.6267361108 + -1.583333333x + x2 = 0.0642361108 Factor a perfect square on the left side: (x + -0.7916666665)(x + -0.7916666665) = 0.0642361108 Calculate the square root of the right side: 0.253448438 Break this problem into two subproblems by setting (x + -0.7916666665) equal to 0.253448438 and -0.253448438.Subproblem 1
x + -0.7916666665 = 0.253448438 Simplifying x + -0.7916666665 = 0.253448438 Reorder the terms: -0.7916666665 + x = 0.253448438 Solving -0.7916666665 + x = 0.253448438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + x = 0.253448438 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + x = 0.253448438 + 0.7916666665 x = 0.253448438 + 0.7916666665 Combine like terms: 0.253448438 + 0.7916666665 = 1.0451151045 x = 1.0451151045 Simplifying x = 1.0451151045Subproblem 2
x + -0.7916666665 = -0.253448438 Simplifying x + -0.7916666665 = -0.253448438 Reorder the terms: -0.7916666665 + x = -0.253448438 Solving -0.7916666665 + x = -0.253448438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + x = -0.253448438 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + x = -0.253448438 + 0.7916666665 x = -0.253448438 + 0.7916666665 Combine like terms: -0.253448438 + 0.7916666665 = 0.5382182285 x = 0.5382182285 Simplifying x = 0.5382182285Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0451151045, 0.5382182285}
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