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Simplifying 9x2 + -3x + 4 = 15x Reorder the terms: 4 + -3x + 9x2 = 15x Solving 4 + -3x + 9x2 = 15x Solving for variable 'x'. Reorder the terms: 4 + -3x + -15x + 9x2 = 15x + -15x Combine like terms: -3x + -15x = -18x 4 + -18x + 9x2 = 15x + -15x Combine like terms: 15x + -15x = 0 4 + -18x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + -2x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -2x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -2x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.4444444444 -2x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -2x + x2 = -0.4444444444 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.4444444444 + 1 Reorder the terms: 1 + -2x + x2 = -0.4444444444 + 1 Combine like terms: -0.4444444444 + 1 = 0.5555555556 1 + -2x + x2 = 0.5555555556 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.5555555556 Calculate the square root of the right side: 0.745355993 Break this problem into two subproblems by setting (x + -1) equal to 0.745355993 and -0.745355993.Subproblem 1
x + -1 = 0.745355993 Simplifying x + -1 = 0.745355993 Reorder the terms: -1 + x = 0.745355993 Solving -1 + x = 0.745355993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.745355993 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.745355993 + 1 x = 0.745355993 + 1 Combine like terms: 0.745355993 + 1 = 1.745355993 x = 1.745355993 Simplifying x = 1.745355993Subproblem 2
x + -1 = -0.745355993 Simplifying x + -1 = -0.745355993 Reorder the terms: -1 + x = -0.745355993 Solving -1 + x = -0.745355993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.745355993 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.745355993 + 1 x = -0.745355993 + 1 Combine like terms: -0.745355993 + 1 = 0.254644007 x = 0.254644007 Simplifying x = 0.254644007Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.745355993, 0.254644007}
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