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Simplifying 9x(5x + -4) + -4 = 36 Reorder the terms: 9x(-4 + 5x) + -4 = 36 (-4 * 9x + 5x * 9x) + -4 = 36 (-36x + 45x2) + -4 = 36 Reorder the terms: -4 + -36x + 45x2 = 36 Solving -4 + -36x + 45x2 = 36 Solving for variable 'x'. Reorder the terms: -4 + -36 + -36x + 45x2 = 36 + -36 Combine like terms: -4 + -36 = -40 -40 + -36x + 45x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -40 + -36x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.8888888889 + -0.8x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -0.8x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -0.8x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -0.8x + x2 = 0 + 0.8888888889 -0.8x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -0.8x + x2 = 0.8888888889 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 0.8888888889 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 0.8888888889 + 0.16 Combine like terms: 0.8888888889 + 0.16 = 1.0488888889 0.16 + -0.8x + x2 = 1.0488888889 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 1.0488888889 Calculate the square root of the right side: 1.024152766 Break this problem into two subproblems by setting (x + -0.4) equal to 1.024152766 and -1.024152766.Subproblem 1
x + -0.4 = 1.024152766 Simplifying x + -0.4 = 1.024152766 Reorder the terms: -0.4 + x = 1.024152766 Solving -0.4 + x = 1.024152766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.024152766 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.024152766 + 0.4 x = 1.024152766 + 0.4 Combine like terms: 1.024152766 + 0.4 = 1.424152766 x = 1.424152766 Simplifying x = 1.424152766Subproblem 2
x + -0.4 = -1.024152766 Simplifying x + -0.4 = -1.024152766 Reorder the terms: -0.4 + x = -1.024152766 Solving -0.4 + x = -1.024152766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.024152766 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.024152766 + 0.4 x = -1.024152766 + 0.4 Combine like terms: -1.024152766 + 0.4 = -0.624152766 x = -0.624152766 Simplifying x = -0.624152766Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.424152766, -0.624152766}
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