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Simplifying 2x2 + 1.2x + -212 = 0 Reorder the terms: -212 + 1.2x + 2x2 = 0 Solving -212 + 1.2x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -106 + 0.6x + x2 = 0 Move the constant term to the right: Add '106' to each side of the equation. -106 + 0.6x + 106 + x2 = 0 + 106 Reorder the terms: -106 + 106 + 0.6x + x2 = 0 + 106 Combine like terms: -106 + 106 = 0 0 + 0.6x + x2 = 0 + 106 0.6x + x2 = 0 + 106 Combine like terms: 0 + 106 = 106 0.6x + x2 = 106 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 106 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 106 + 0.09 Combine like terms: 106 + 0.09 = 106.09 0.09 + 0.6x + x2 = 106.09 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 106.09 Calculate the square root of the right side: 10.3 Break this problem into two subproblems by setting (x + 0.3) equal to 10.3 and -10.3.Subproblem 1
x + 0.3 = 10.3 Simplifying x + 0.3 = 10.3 Reorder the terms: 0.3 + x = 10.3 Solving 0.3 + x = 10.3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 10.3 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 10.3 + -0.3 x = 10.3 + -0.3 Combine like terms: 10.3 + -0.3 = 10 x = 10 Simplifying x = 10Subproblem 2
x + 0.3 = -10.3 Simplifying x + 0.3 = -10.3 Reorder the terms: 0.3 + x = -10.3 Solving 0.3 + x = -10.3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -10.3 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -10.3 + -0.3 x = -10.3 + -0.3 Combine like terms: -10.3 + -0.3 = -10.6 x = -10.6 Simplifying x = -10.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -10.6}
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