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Simplifying 10x2 + -43x = 30 Reorder the terms: -43x + 10x2 = 30 Solving -43x + 10x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + -43x + 10x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -43x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -3 + -4.3x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -4.3x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -4.3x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4.3x + x2 = 0 + 3 -4.3x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4.3x + x2 = 3 The x term is -4.3x. Take half its coefficient (-2.15). Square it (4.6225) and add it to both sides. Add '4.6225' to each side of the equation. -4.3x + 4.6225 + x2 = 3 + 4.6225 Reorder the terms: 4.6225 + -4.3x + x2 = 3 + 4.6225 Combine like terms: 3 + 4.6225 = 7.6225 4.6225 + -4.3x + x2 = 7.6225 Factor a perfect square on the left side: (x + -2.15)(x + -2.15) = 7.6225 Calculate the square root of the right side: 2.760887538 Break this problem into two subproblems by setting (x + -2.15) equal to 2.760887538 and -2.760887538.Subproblem 1
x + -2.15 = 2.760887538 Simplifying x + -2.15 = 2.760887538 Reorder the terms: -2.15 + x = 2.760887538 Solving -2.15 + x = 2.760887538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.15' to each side of the equation. -2.15 + 2.15 + x = 2.760887538 + 2.15 Combine like terms: -2.15 + 2.15 = 0.00 0.00 + x = 2.760887538 + 2.15 x = 2.760887538 + 2.15 Combine like terms: 2.760887538 + 2.15 = 4.910887538 x = 4.910887538 Simplifying x = 4.910887538Subproblem 2
x + -2.15 = -2.760887538 Simplifying x + -2.15 = -2.760887538 Reorder the terms: -2.15 + x = -2.760887538 Solving -2.15 + x = -2.760887538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.15' to each side of the equation. -2.15 + 2.15 + x = -2.760887538 + 2.15 Combine like terms: -2.15 + 2.15 = 0.00 0.00 + x = -2.760887538 + 2.15 x = -2.760887538 + 2.15 Combine like terms: -2.760887538 + 2.15 = -0.610887538 x = -0.610887538 Simplifying x = -0.610887538Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.910887538, -0.610887538}
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