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Simplifying 3x(5x + -9) = 79 Reorder the terms: 3x(-9 + 5x) = 79 (-9 * 3x + 5x * 3x) = 79 (-27x + 15x2) = 79 Solving -27x + 15x2 = 79 Solving for variable 'x'. Reorder the terms: -79 + -27x + 15x2 = 79 + -79 Combine like terms: 79 + -79 = 0 -79 + -27x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -5.266666667 + -1.8x + x2 = 0 Move the constant term to the right: Add '5.266666667' to each side of the equation. -5.266666667 + -1.8x + 5.266666667 + x2 = 0 + 5.266666667 Reorder the terms: -5.266666667 + 5.266666667 + -1.8x + x2 = 0 + 5.266666667 Combine like terms: -5.266666667 + 5.266666667 = 0.000000000 0.000000000 + -1.8x + x2 = 0 + 5.266666667 -1.8x + x2 = 0 + 5.266666667 Combine like terms: 0 + 5.266666667 = 5.266666667 -1.8x + x2 = 5.266666667 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = 5.266666667 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 5.266666667 + 0.81 Combine like terms: 5.266666667 + 0.81 = 6.076666667 0.81 + -1.8x + x2 = 6.076666667 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 6.076666667 Calculate the square root of the right side: 2.465089586 Break this problem into two subproblems by setting (x + -0.9) equal to 2.465089586 and -2.465089586.Subproblem 1
x + -0.9 = 2.465089586 Simplifying x + -0.9 = 2.465089586 Reorder the terms: -0.9 + x = 2.465089586 Solving -0.9 + x = 2.465089586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 2.465089586 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 2.465089586 + 0.9 x = 2.465089586 + 0.9 Combine like terms: 2.465089586 + 0.9 = 3.365089586 x = 3.365089586 Simplifying x = 3.365089586Subproblem 2
x + -0.9 = -2.465089586 Simplifying x + -0.9 = -2.465089586 Reorder the terms: -0.9 + x = -2.465089586 Solving -0.9 + x = -2.465089586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -2.465089586 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -2.465089586 + 0.9 x = -2.465089586 + 0.9 Combine like terms: -2.465089586 + 0.9 = -1.565089586 x = -1.565089586 Simplifying x = -1.565089586Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.365089586, -1.565089586}
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