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Simplifying 3x + 5x(5 + 9x) = 6(4 + 5) 3x + (5 * 5x + 9x * 5x) = 6(4 + 5) 3x + (25x + 45x2) = 6(4 + 5) Combine like terms: 3x + 25x = 28x 28x + 45x2 = 6(4 + 5) Combine like terms: 4 + 5 = 9 28x + 45x2 = 6(9) Multiply 6 * 9 28x + 45x2 = 54 Solving 28x + 45x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + 28x + 45x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 28x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -1.2 + 0.6222222222x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 0.6222222222x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 0.6222222222x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 0.6222222222x + x2 = 0 + 1.2 0.6222222222x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 0.6222222222x + x2 = 1.2 The x term is 0.6222222222x. Take half its coefficient (0.3111111111). Square it (0.09679012345) and add it to both sides. Add '0.09679012345' to each side of the equation. 0.6222222222x + 0.09679012345 + x2 = 1.2 + 0.09679012345 Reorder the terms: 0.09679012345 + 0.6222222222x + x2 = 1.2 + 0.09679012345 Combine like terms: 1.2 + 0.09679012345 = 1.29679012345 0.09679012345 + 0.6222222222x + x2 = 1.29679012345 Factor a perfect square on the left side: (x + 0.3111111111)(x + 0.3111111111) = 1.29679012345 Calculate the square root of the right side: 1.138766931 Break this problem into two subproblems by setting (x + 0.3111111111) equal to 1.138766931 and -1.138766931.Subproblem 1
x + 0.3111111111 = 1.138766931 Simplifying x + 0.3111111111 = 1.138766931 Reorder the terms: 0.3111111111 + x = 1.138766931 Solving 0.3111111111 + x = 1.138766931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3111111111' to each side of the equation. 0.3111111111 + -0.3111111111 + x = 1.138766931 + -0.3111111111 Combine like terms: 0.3111111111 + -0.3111111111 = 0.0000000000 0.0000000000 + x = 1.138766931 + -0.3111111111 x = 1.138766931 + -0.3111111111 Combine like terms: 1.138766931 + -0.3111111111 = 0.8276558199 x = 0.8276558199 Simplifying x = 0.8276558199Subproblem 2
x + 0.3111111111 = -1.138766931 Simplifying x + 0.3111111111 = -1.138766931 Reorder the terms: 0.3111111111 + x = -1.138766931 Solving 0.3111111111 + x = -1.138766931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3111111111' to each side of the equation. 0.3111111111 + -0.3111111111 + x = -1.138766931 + -0.3111111111 Combine like terms: 0.3111111111 + -0.3111111111 = 0.0000000000 0.0000000000 + x = -1.138766931 + -0.3111111111 x = -1.138766931 + -0.3111111111 Combine like terms: -1.138766931 + -0.3111111111 = -1.4498780421 x = -1.4498780421 Simplifying x = -1.4498780421Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8276558199, -1.4498780421}
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