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Simplifying 63x2 + -40x = 90 Reorder the terms: -40x + 63x2 = 90 Solving -40x + 63x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -40x + 63x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -40x + 63x2 = 0 Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -1.428571429 + -0.6349206349x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -0.6349206349x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -0.6349206349x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -0.6349206349x + x2 = 0 + 1.428571429 -0.6349206349x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -0.6349206349x + x2 = 1.428571429 The x term is -0.6349206349x. Take half its coefficient (-0.3174603175). Square it (0.1007810532) and add it to both sides. Add '0.1007810532' to each side of the equation. -0.6349206349x + 0.1007810532 + x2 = 1.428571429 + 0.1007810532 Reorder the terms: 0.1007810532 + -0.6349206349x + x2 = 1.428571429 + 0.1007810532 Combine like terms: 1.428571429 + 0.1007810532 = 1.5293524822 0.1007810532 + -0.6349206349x + x2 = 1.5293524822 Factor a perfect square on the left side: (x + -0.3174603175)(x + -0.3174603175) = 1.5293524822 Calculate the square root of the right side: 1.236669916 Break this problem into two subproblems by setting (x + -0.3174603175) equal to 1.236669916 and -1.236669916.Subproblem 1
x + -0.3174603175 = 1.236669916 Simplifying x + -0.3174603175 = 1.236669916 Reorder the terms: -0.3174603175 + x = 1.236669916 Solving -0.3174603175 + x = 1.236669916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3174603175' to each side of the equation. -0.3174603175 + 0.3174603175 + x = 1.236669916 + 0.3174603175 Combine like terms: -0.3174603175 + 0.3174603175 = 0.0000000000 0.0000000000 + x = 1.236669916 + 0.3174603175 x = 1.236669916 + 0.3174603175 Combine like terms: 1.236669916 + 0.3174603175 = 1.5541302335 x = 1.5541302335 Simplifying x = 1.5541302335Subproblem 2
x + -0.3174603175 = -1.236669916 Simplifying x + -0.3174603175 = -1.236669916 Reorder the terms: -0.3174603175 + x = -1.236669916 Solving -0.3174603175 + x = -1.236669916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3174603175' to each side of the equation. -0.3174603175 + 0.3174603175 + x = -1.236669916 + 0.3174603175 Combine like terms: -0.3174603175 + 0.3174603175 = 0.0000000000 0.0000000000 + x = -1.236669916 + 0.3174603175 x = -1.236669916 + 0.3174603175 Combine like terms: -1.236669916 + 0.3174603175 = -0.9192095985 x = -0.9192095985 Simplifying x = -0.9192095985Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5541302335, -0.9192095985}
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