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Simplifying 5x2 + 3x + -7 = 12 Reorder the terms: -7 + 3x + 5x2 = 12 Solving -7 + 3x + 5x2 = 12 Solving for variable 'x'. Reorder the terms: -7 + -12 + 3x + 5x2 = 12 + -12 Combine like terms: -7 + -12 = -19 -19 + 3x + 5x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -19 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.8 + 0.6x + x2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + 0.6x + 3.8 + x2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + 0.6x + x2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + 0.6x + x2 = 0 + 3.8 0.6x + x2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 0.6x + x2 = 3.8 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 = 3.8 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 3.8 + 0.09 Combine like terms: 3.8 + 0.09 = 3.89 0.09 + 0.6x + x2 = 3.89 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 3.89 Calculate the square root of the right side: 1.972308292 Break this problem into two subproblems by setting (x + 0.3) equal to 1.972308292 and -1.972308292.Subproblem 1
x + 0.3 = 1.972308292 Simplifying x + 0.3 = 1.972308292 Reorder the terms: 0.3 + x = 1.972308292 Solving 0.3 + x = 1.972308292 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 = 1.972308292 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.972308292 + -0.3 x = 1.972308292 + -0.3 Combine like terms: 1.972308292 + -0.3 = 1.672308292 x = 1.672308292 Simplifying x = 1.672308292Subproblem 2
x + 0.3 = -1.972308292 Simplifying x + 0.3 = -1.972308292 Reorder the terms: 0.3 + x = -1.972308292 Solving 0.3 + x = -1.972308292 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 = -1.972308292 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.972308292 + -0.3 x = -1.972308292 + -0.3 Combine like terms: -1.972308292 + -0.3 = -2.272308292 x = -2.272308292 Simplifying x = -2.272308292Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.672308292, -2.272308292}
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