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Simplifying 10x2 + 9 = 15x(x + -2) Reorder the terms: 9 + 10x2 = 15x(x + -2) Reorder the terms: 9 + 10x2 = 15x(-2 + x) 9 + 10x2 = (-2 * 15x + x * 15x) 9 + 10x2 = (-30x + 15x2) Solving 9 + 10x2 = -30x + 15x2 Solving for variable 'x'. Reorder the terms: 9 + 30x + 10x2 + -15x2 = -30x + 15x2 + 30x + -15x2 Combine like terms: 10x2 + -15x2 = -5x2 9 + 30x + -5x2 = -30x + 15x2 + 30x + -15x2 Reorder the terms: 9 + 30x + -5x2 = -30x + 30x + 15x2 + -15x2 Combine like terms: -30x + 30x = 0 9 + 30x + -5x2 = 0 + 15x2 + -15x2 9 + 30x + -5x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 9 + 30x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.8 + -6x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -6x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -6x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -6x + x2 = 0 + 1.8 -6x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -6x + x2 = 1.8 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 1.8 + 9 Reorder the terms: 9 + -6x + x2 = 1.8 + 9 Combine like terms: 1.8 + 9 = 10.8 9 + -6x + x2 = 10.8 Factor a perfect square on the left side: (x + -3)(x + -3) = 10.8 Calculate the square root of the right side: 3.286335345 Break this problem into two subproblems by setting (x + -3) equal to 3.286335345 and -3.286335345.Subproblem 1
x + -3 = 3.286335345 Simplifying x + -3 = 3.286335345 Reorder the terms: -3 + x = 3.286335345 Solving -3 + x = 3.286335345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.286335345 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.286335345 + 3 x = 3.286335345 + 3 Combine like terms: 3.286335345 + 3 = 6.286335345 x = 6.286335345 Simplifying x = 6.286335345Subproblem 2
x + -3 = -3.286335345 Simplifying x + -3 = -3.286335345 Reorder the terms: -3 + x = -3.286335345 Solving -3 + x = -3.286335345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.286335345 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.286335345 + 3 x = -3.286335345 + 3 Combine like terms: -3.286335345 + 3 = -0.286335345 x = -0.286335345 Simplifying x = -0.286335345Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.286335345, -0.286335345}
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