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Simplifying 15 + (3x + -5)(12x + 5) = 0 Reorder the terms: 15 + (-5 + 3x)(12x + 5) = 0 Reorder the terms: 15 + (-5 + 3x)(5 + 12x) = 0 Multiply (-5 + 3x) * (5 + 12x) 15 + (-5(5 + 12x) + 3x * (5 + 12x)) = 0 15 + ((5 * -5 + 12x * -5) + 3x * (5 + 12x)) = 0 15 + ((-25 + -60x) + 3x * (5 + 12x)) = 0 15 + (-25 + -60x + (5 * 3x + 12x * 3x)) = 0 15 + (-25 + -60x + (15x + 36x2)) = 0 Combine like terms: -60x + 15x = -45x 15 + (-25 + -45x + 36x2) = 0 Combine like terms: 15 + -25 = -10 -10 + -45x + 36x2 = 0 Solving -10 + -45x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.2777777778 + -1.25x + x2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + -1.25x + 0.2777777778 + x2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + -1.25x + x2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + -1.25x + x2 = 0 + 0.2777777778 -1.25x + x2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 -1.25x + x2 = 0.2777777778 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 0.2777777778 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 0.2777777778 + 0.390625 Combine like terms: 0.2777777778 + 0.390625 = 0.6684027778 0.390625 + -1.25x + x2 = 0.6684027778 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.6684027778 Calculate the square root of the right side: 0.817559036 Break this problem into two subproblems by setting (x + -0.625) equal to 0.817559036 and -0.817559036.Subproblem 1
x + -0.625 = 0.817559036 Simplifying x + -0.625 = 0.817559036 Reorder the terms: -0.625 + x = 0.817559036 Solving -0.625 + x = 0.817559036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 0.817559036 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.817559036 + 0.625 x = 0.817559036 + 0.625 Combine like terms: 0.817559036 + 0.625 = 1.442559036 x = 1.442559036 Simplifying x = 1.442559036Subproblem 2
x + -0.625 = -0.817559036 Simplifying x + -0.625 = -0.817559036 Reorder the terms: -0.625 + x = -0.817559036 Solving -0.625 + x = -0.817559036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -0.817559036 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.817559036 + 0.625 x = -0.817559036 + 0.625 Combine like terms: -0.817559036 + 0.625 = -0.192559036 x = -0.192559036 Simplifying x = -0.192559036Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.442559036, -0.192559036}
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