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Simplifying 4x2 + -30x + -45 = 0 Reorder the terms: -45 + -30x + 4x2 = 0 Solving -45 + -30x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.25 + -7.5x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -7.5x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -7.5x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -7.5x + x2 = 0 + 11.25 -7.5x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -7.5x + x2 = 11.25 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 11.25 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 11.25 + 14.0625 Combine like terms: 11.25 + 14.0625 = 25.3125 14.0625 + -7.5x + x2 = 25.3125 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 25.3125 Calculate the square root of the right side: 5.031152949 Break this problem into two subproblems by setting (x + -3.75) equal to 5.031152949 and -5.031152949.Subproblem 1
x + -3.75 = 5.031152949 Simplifying x + -3.75 = 5.031152949 Reorder the terms: -3.75 + x = 5.031152949 Solving -3.75 + x = 5.031152949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 5.031152949 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 5.031152949 + 3.75 x = 5.031152949 + 3.75 Combine like terms: 5.031152949 + 3.75 = 8.781152949 x = 8.781152949 Simplifying x = 8.781152949Subproblem 2
x + -3.75 = -5.031152949 Simplifying x + -3.75 = -5.031152949 Reorder the terms: -3.75 + x = -5.031152949 Solving -3.75 + x = -5.031152949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -5.031152949 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -5.031152949 + 3.75 x = -5.031152949 + 3.75 Combine like terms: -5.031152949 + 3.75 = -1.281152949 x = -1.281152949 Simplifying x = -1.281152949Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.781152949, -1.281152949}
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