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Simplifying 3x2 + 79x = -30 Reorder the terms: 79x + 3x2 = -30 Solving 79x + 3x2 = -30 Solving for variable 'x'. Reorder the terms: 30 + 79x + 3x2 = -30 + 30 Combine like terms: -30 + 30 = 0 30 + 79x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10 + 26.33333333x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 26.33333333x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 26.33333333x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 26.33333333x + x2 = 0 + -10 26.33333333x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 26.33333333x + x2 = -10 The x term is 26.33333333x. Take half its coefficient (13.16666667). Square it (173.3611112) and add it to both sides. Add '173.3611112' to each side of the equation. 26.33333333x + 173.3611112 + x2 = -10 + 173.3611112 Reorder the terms: 173.3611112 + 26.33333333x + x2 = -10 + 173.3611112 Combine like terms: -10 + 173.3611112 = 163.3611112 173.3611112 + 26.33333333x + x2 = 163.3611112 Factor a perfect square on the left side: (x + 13.16666667)(x + 13.16666667) = 163.3611112 Calculate the square root of the right side: 12.781279717 Break this problem into two subproblems by setting (x + 13.16666667) equal to 12.781279717 and -12.781279717.Subproblem 1
x + 13.16666667 = 12.781279717 Simplifying x + 13.16666667 = 12.781279717 Reorder the terms: 13.16666667 + x = 12.781279717 Solving 13.16666667 + x = 12.781279717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.16666667' to each side of the equation. 13.16666667 + -13.16666667 + x = 12.781279717 + -13.16666667 Combine like terms: 13.16666667 + -13.16666667 = 0.00000000 0.00000000 + x = 12.781279717 + -13.16666667 x = 12.781279717 + -13.16666667 Combine like terms: 12.781279717 + -13.16666667 = -0.385386953 x = -0.385386953 Simplifying x = -0.385386953Subproblem 2
x + 13.16666667 = -12.781279717 Simplifying x + 13.16666667 = -12.781279717 Reorder the terms: 13.16666667 + x = -12.781279717 Solving 13.16666667 + x = -12.781279717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.16666667' to each side of the equation. 13.16666667 + -13.16666667 + x = -12.781279717 + -13.16666667 Combine like terms: 13.16666667 + -13.16666667 = 0.00000000 0.00000000 + x = -12.781279717 + -13.16666667 x = -12.781279717 + -13.16666667 Combine like terms: -12.781279717 + -13.16666667 = -25.947946387 x = -25.947946387 Simplifying x = -25.947946387Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.385386953, -25.947946387}
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