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Simplifying 3x2 + -45x = 152 Reorder the terms: -45x + 3x2 = 152 Solving -45x + 3x2 = 152 Solving for variable 'x'. Reorder the terms: -152 + -45x + 3x2 = 152 + -152 Combine like terms: 152 + -152 = 0 -152 + -45x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -50.66666667 + -15x + x2 = 0 Move the constant term to the right: Add '50.66666667' to each side of the equation. -50.66666667 + -15x + 50.66666667 + x2 = 0 + 50.66666667 Reorder the terms: -50.66666667 + 50.66666667 + -15x + x2 = 0 + 50.66666667 Combine like terms: -50.66666667 + 50.66666667 = 0.00000000 0.00000000 + -15x + x2 = 0 + 50.66666667 -15x + x2 = 0 + 50.66666667 Combine like terms: 0 + 50.66666667 = 50.66666667 -15x + x2 = 50.66666667 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 50.66666667 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 50.66666667 + 56.25 Combine like terms: 50.66666667 + 56.25 = 106.91666667 56.25 + -15x + x2 = 106.91666667 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 106.91666667 Calculate the square root of the right side: 10.34005158 Break this problem into two subproblems by setting (x + -7.5) equal to 10.34005158 and -10.34005158.Subproblem 1
x + -7.5 = 10.34005158 Simplifying x + -7.5 = 10.34005158 Reorder the terms: -7.5 + x = 10.34005158 Solving -7.5 + x = 10.34005158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 10.34005158 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 10.34005158 + 7.5 x = 10.34005158 + 7.5 Combine like terms: 10.34005158 + 7.5 = 17.84005158 x = 17.84005158 Simplifying x = 17.84005158Subproblem 2
x + -7.5 = -10.34005158 Simplifying x + -7.5 = -10.34005158 Reorder the terms: -7.5 + x = -10.34005158 Solving -7.5 + x = -10.34005158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -10.34005158 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -10.34005158 + 7.5 x = -10.34005158 + 7.5 Combine like terms: -10.34005158 + 7.5 = -2.84005158 x = -2.84005158 Simplifying x = -2.84005158Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.84005158, -2.84005158}
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