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Simplifying 0 = (0.3x + 6)(0.3x + 6) + -5 Reorder the terms: 0 = (6 + 0.3x)(0.3x + 6) + -5 Reorder the terms: 0 = (6 + 0.3x)(6 + 0.3x) + -5 Multiply (6 + 0.3x) * (6 + 0.3x) 0 = (6(6 + 0.3x) + 0.3x * (6 + 0.3x)) + -5 0 = ((6 * 6 + 0.3x * 6) + 0.3x * (6 + 0.3x)) + -5 0 = ((36 + 1.8x) + 0.3x * (6 + 0.3x)) + -5 0 = (36 + 1.8x + (6 * 0.3x + 0.3x * 0.3x)) + -5 0 = (36 + 1.8x + (1.8x + 0.09x2)) + -5 Combine like terms: 1.8x + 1.8x = 3.6x 0 = (36 + 3.6x + 0.09x2) + -5 Reorder the terms: 0 = 36 + -5 + 3.6x + 0.09x2 Combine like terms: 36 + -5 = 31 0 = 31 + 3.6x + 0.09x2 Solving 0 = 31 + 3.6x + 0.09x2 Solving for variable 'x'. Combine like terms: 0 + -31 = -31 -31 + -3.6x + -0.09x2 = 31 + 3.6x + 0.09x2 + -31 + -3.6x + -0.09x2 Reorder the terms: -31 + -3.6x + -0.09x2 = 31 + -31 + 3.6x + -3.6x + 0.09x2 + -0.09x2 Combine like terms: 31 + -31 = 0 -31 + -3.6x + -0.09x2 = 0 + 3.6x + -3.6x + 0.09x2 + -0.09x2 -31 + -3.6x + -0.09x2 = 3.6x + -3.6x + 0.09x2 + -0.09x2 Combine like terms: 3.6x + -3.6x = 0.0 -31 + -3.6x + -0.09x2 = 0.0 + 0.09x2 + -0.09x2 -31 + -3.6x + -0.09x2 = 0.09x2 + -0.09x2 Combine like terms: 0.09x2 + -0.09x2 = 0.00 -31 + -3.6x + -0.09x2 = 0.00 Begin completing the square. Divide all terms by -0.09 the coefficient of the squared term: Divide each side by '-0.09'. 344.4444444 + 40x + x2 = 0 Move the constant term to the right: Add '-344.4444444' to each side of the equation. 344.4444444 + 40x + -344.4444444 + x2 = 0 + -344.4444444 Reorder the terms: 344.4444444 + -344.4444444 + 40x + x2 = 0 + -344.4444444 Combine like terms: 344.4444444 + -344.4444444 = 0.0000000 0.0000000 + 40x + x2 = 0 + -344.4444444 40x + x2 = 0 + -344.4444444 Combine like terms: 0 + -344.4444444 = -344.4444444 40x + x2 = -344.4444444 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = -344.4444444 + 400 Reorder the terms: 400 + 40x + x2 = -344.4444444 + 400 Combine like terms: -344.4444444 + 400 = 55.5555556 400 + 40x + x2 = 55.5555556 Factor a perfect square on the left side: (x + 20)(x + 20) = 55.5555556 Calculate the square root of the right side: 7.453559928 Break this problem into two subproblems by setting (x + 20) equal to 7.453559928 and -7.453559928.Subproblem 1
x + 20 = 7.453559928 Simplifying x + 20 = 7.453559928 Reorder the terms: 20 + x = 7.453559928 Solving 20 + x = 7.453559928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 7.453559928 + -20 Combine like terms: 20 + -20 = 0 0 + x = 7.453559928 + -20 x = 7.453559928 + -20 Combine like terms: 7.453559928 + -20 = -12.546440072 x = -12.546440072 Simplifying x = -12.546440072Subproblem 2
x + 20 = -7.453559928 Simplifying x + 20 = -7.453559928 Reorder the terms: 20 + x = -7.453559928 Solving 20 + x = -7.453559928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -7.453559928 + -20 Combine like terms: 20 + -20 = 0 0 + x = -7.453559928 + -20 x = -7.453559928 + -20 Combine like terms: -7.453559928 + -20 = -27.453559928 x = -27.453559928 Simplifying x = -27.453559928Solution
The solution to the problem is based on the solutions from the subproblems. x = {-12.546440072, -27.453559928}
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