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Simplifying 10x2 + 6x + -21 = -12 Reorder the terms: -21 + 6x + 10x2 = -12 Solving -21 + 6x + 10x2 = -12 Solving for variable 'x'. Reorder the terms: -21 + 12 + 6x + 10x2 = -12 + 12 Combine like terms: -21 + 12 = -9 -9 + 6x + 10x2 = -12 + 12 Combine like terms: -12 + 12 = 0 -9 + 6x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + 0.6x + x2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 0.6x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + 0.6x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 0.6x + x2 = 0 + 0.9 0.6x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 0.6x + x2 = 0.9 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 = 0.9 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 0.9 + 0.09 Combine like terms: 0.9 + 0.09 = 0.99 0.09 + 0.6x + x2 = 0.99 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 0.99 Calculate the square root of the right side: 0.994987437 Break this problem into two subproblems by setting (x + 0.3) equal to 0.994987437 and -0.994987437.Subproblem 1
x + 0.3 = 0.994987437 Simplifying x + 0.3 = 0.994987437 Reorder the terms: 0.3 + x = 0.994987437 Solving 0.3 + x = 0.994987437 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 = 0.994987437 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.994987437 + -0.3 x = 0.994987437 + -0.3 Combine like terms: 0.994987437 + -0.3 = 0.694987437 x = 0.694987437 Simplifying x = 0.694987437Subproblem 2
x + 0.3 = -0.994987437 Simplifying x + 0.3 = -0.994987437 Reorder the terms: 0.3 + x = -0.994987437 Solving 0.3 + x = -0.994987437 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 = -0.994987437 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -0.994987437 + -0.3 x = -0.994987437 + -0.3 Combine like terms: -0.994987437 + -0.3 = -1.294987437 x = -1.294987437 Simplifying x = -1.294987437Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.694987437, -1.294987437}
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