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Simplifying 4x2 + -3x + 9 = 15x Reorder the terms: 9 + -3x + 4x2 = 15x Solving 9 + -3x + 4x2 = 15x Solving for variable 'x'. Reorder the terms: 9 + -3x + -15x + 4x2 = 15x + -15x Combine like terms: -3x + -15x = -18x 9 + -18x + 4x2 = 15x + -15x Combine like terms: 15x + -15x = 0 9 + -18x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -4.5x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -4.5x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -4.5x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -4.5x + x2 = 0 + -2.25 -4.5x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -4.5x + x2 = -2.25 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -2.25 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -2.25 + 5.0625 Combine like terms: -2.25 + 5.0625 = 2.8125 5.0625 + -4.5x + x2 = 2.8125 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 2.8125 Calculate the square root of the right side: 1.677050983 Break this problem into two subproblems by setting (x + -2.25) equal to 1.677050983 and -1.677050983.Subproblem 1
x + -2.25 = 1.677050983 Simplifying x + -2.25 = 1.677050983 Reorder the terms: -2.25 + x = 1.677050983 Solving -2.25 + x = 1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.677050983 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.677050983 + 2.25 x = 1.677050983 + 2.25 Combine like terms: 1.677050983 + 2.25 = 3.927050983 x = 3.927050983 Simplifying x = 3.927050983Subproblem 2
x + -2.25 = -1.677050983 Simplifying x + -2.25 = -1.677050983 Reorder the terms: -2.25 + x = -1.677050983 Solving -2.25 + x = -1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.677050983 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.677050983 + 2.25 x = -1.677050983 + 2.25 Combine like terms: -1.677050983 + 2.25 = 0.572949017 x = 0.572949017 Simplifying x = 0.572949017Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.927050983, 0.572949017}
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