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Simplifying 10x2 + -93 = 20x Reorder the terms: -93 + 10x2 = 20x Solving -93 + 10x2 = 20x Solving for variable 'x'. Reorder the terms: -93 + -20x + 10x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -93 + -20x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -9.3 + -2x + x2 = 0 Move the constant term to the right: Add '9.3' to each side of the equation. -9.3 + -2x + 9.3 + x2 = 0 + 9.3 Reorder the terms: -9.3 + 9.3 + -2x + x2 = 0 + 9.3 Combine like terms: -9.3 + 9.3 = 0.0 0.0 + -2x + x2 = 0 + 9.3 -2x + x2 = 0 + 9.3 Combine like terms: 0 + 9.3 = 9.3 -2x + x2 = 9.3 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 = 9.3 + 1 Reorder the terms: 1 + -2x + x2 = 9.3 + 1 Combine like terms: 9.3 + 1 = 10.3 1 + -2x + x2 = 10.3 Factor a perfect square on the left side: (x + -1)(x + -1) = 10.3 Calculate the square root of the right side: 3.209361307 Break this problem into two subproblems by setting (x + -1) equal to 3.209361307 and -3.209361307.Subproblem 1
x + -1 = 3.209361307 Simplifying x + -1 = 3.209361307 Reorder the terms: -1 + x = 3.209361307 Solving -1 + x = 3.209361307 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 = 3.209361307 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.209361307 + 1 x = 3.209361307 + 1 Combine like terms: 3.209361307 + 1 = 4.209361307 x = 4.209361307 Simplifying x = 4.209361307Subproblem 2
x + -1 = -3.209361307 Simplifying x + -1 = -3.209361307 Reorder the terms: -1 + x = -3.209361307 Solving -1 + x = -3.209361307 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 = -3.209361307 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.209361307 + 1 x = -3.209361307 + 1 Combine like terms: -3.209361307 + 1 = -2.209361307 x = -2.209361307 Simplifying x = -2.209361307Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.209361307, -2.209361307}
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