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Simplifying (4x2) + -1(30x) + 45 = 0 Remove parenthesis around (30x) (4x2) + -1 * 30x + 45 = 0 Multiply -1 * 30 (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 = 2.8125 14.0625 + -7.5x + x2 = 2.8125 Factor a perfect square on the left side: ((x) + -3.75)((x) + -3.75) = 2.8125 Calculate the square root of the right side: 1.677050983 Break this problem into two subproblems by setting ((x) + -3.75) equal to 1.677050983 and -1.677050983.Subproblem 1
(x) + -3.75 = 1.677050983 Simplifying (x) + -3.75 = 1.677050983 x + -3.75 = 1.677050983 Reorder the terms: -3.75 + x = 1.677050983 Solving -3.75 + x = 1.677050983 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 = 1.677050983 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 1.677050983 + 3.75 x = 1.677050983 + 3.75 Combine like terms: 1.677050983 + 3.75 = 5.427050983 x = 5.427050983 Simplifying x = 5.427050983Subproblem 2
(x) + -3.75 = -1.677050983 Simplifying (x) + -3.75 = -1.677050983 x + -3.75 = -1.677050983 Reorder the terms: -3.75 + x = -1.677050983 Solving -3.75 + x = -1.677050983 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 = -1.677050983 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -1.677050983 + 3.75 x = -1.677050983 + 3.75 Combine like terms: -1.677050983 + 3.75 = 2.072949017 x = 2.072949017 Simplifying x = 2.072949017Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.427050983, 2.072949017}
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