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Simplifying 10x2 + 2x + -195 = 0 Reorder the terms: -195 + 2x + 10x2 = 0 Solving -195 + 2x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -19.5 + 0.2x + x2 = 0 Move the constant term to the right: Add '19.5' to each side of the equation. -19.5 + 0.2x + 19.5 + x2 = 0 + 19.5 Reorder the terms: -19.5 + 19.5 + 0.2x + x2 = 0 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + 0.2x + x2 = 0 + 19.5 0.2x + x2 = 0 + 19.5 Combine like terms: 0 + 19.5 = 19.5 0.2x + x2 = 19.5 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 19.5 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 19.5 + 0.01 Combine like terms: 19.5 + 0.01 = 19.51 0.01 + 0.2x + x2 = 19.51 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 19.51 Calculate the square root of the right side: 4.417012565 Break this problem into two subproblems by setting (x + 0.1) equal to 4.417012565 and -4.417012565.Subproblem 1
x + 0.1 = 4.417012565 Simplifying x + 0.1 = 4.417012565 Reorder the terms: 0.1 + x = 4.417012565 Solving 0.1 + x = 4.417012565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 4.417012565 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 4.417012565 + -0.1 x = 4.417012565 + -0.1 Combine like terms: 4.417012565 + -0.1 = 4.317012565 x = 4.317012565 Simplifying x = 4.317012565Subproblem 2
x + 0.1 = -4.417012565 Simplifying x + 0.1 = -4.417012565 Reorder the terms: 0.1 + x = -4.417012565 Solving 0.1 + x = -4.417012565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -4.417012565 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -4.417012565 + -0.1 x = -4.417012565 + -0.1 Combine like terms: -4.417012565 + -0.1 = -4.517012565 x = -4.517012565 Simplifying x = -4.517012565Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.317012565, -4.517012565}
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