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Simplifying 19x2 + 12x = 32 Reorder the terms: 12x + 19x2 = 32 Solving 12x + 19x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 12x + 19x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 12x + 19x2 = 0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -1.684210526 + 0.6315789474x + x2 = 0 Move the constant term to the right: Add '1.684210526' to each side of the equation. -1.684210526 + 0.6315789474x + 1.684210526 + x2 = 0 + 1.684210526 Reorder the terms: -1.684210526 + 1.684210526 + 0.6315789474x + x2 = 0 + 1.684210526 Combine like terms: -1.684210526 + 1.684210526 = 0.000000000 0.000000000 + 0.6315789474x + x2 = 0 + 1.684210526 0.6315789474x + x2 = 0 + 1.684210526 Combine like terms: 0 + 1.684210526 = 1.684210526 0.6315789474x + x2 = 1.684210526 The x term is 0.6315789474x. Take half its coefficient (0.3157894737). Square it (0.09972299170) and add it to both sides. Add '0.09972299170' to each side of the equation. 0.6315789474x + 0.09972299170 + x2 = 1.684210526 + 0.09972299170 Reorder the terms: 0.09972299170 + 0.6315789474x + x2 = 1.684210526 + 0.09972299170 Combine like terms: 1.684210526 + 0.09972299170 = 1.7839335177 0.09972299170 + 0.6315789474x + x2 = 1.7839335177 Factor a perfect square on the left side: (x + 0.3157894737)(x + 0.3157894737) = 1.7839335177 Calculate the square root of the right side: 1.335639741 Break this problem into two subproblems by setting (x + 0.3157894737) equal to 1.335639741 and -1.335639741.Subproblem 1
x + 0.3157894737 = 1.335639741 Simplifying x + 0.3157894737 = 1.335639741 Reorder the terms: 0.3157894737 + x = 1.335639741 Solving 0.3157894737 + x = 1.335639741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3157894737' to each side of the equation. 0.3157894737 + -0.3157894737 + x = 1.335639741 + -0.3157894737 Combine like terms: 0.3157894737 + -0.3157894737 = 0.0000000000 0.0000000000 + x = 1.335639741 + -0.3157894737 x = 1.335639741 + -0.3157894737 Combine like terms: 1.335639741 + -0.3157894737 = 1.0198502673 x = 1.0198502673 Simplifying x = 1.0198502673Subproblem 2
x + 0.3157894737 = -1.335639741 Simplifying x + 0.3157894737 = -1.335639741 Reorder the terms: 0.3157894737 + x = -1.335639741 Solving 0.3157894737 + x = -1.335639741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3157894737' to each side of the equation. 0.3157894737 + -0.3157894737 + x = -1.335639741 + -0.3157894737 Combine like terms: 0.3157894737 + -0.3157894737 = 0.0000000000 0.0000000000 + x = -1.335639741 + -0.3157894737 x = -1.335639741 + -0.3157894737 Combine like terms: -1.335639741 + -0.3157894737 = -1.6514292147 x = -1.6514292147 Simplifying x = -1.6514292147Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0198502673, -1.6514292147}
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