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Simplifying 2.5x2 + -3.7x + -4.3 = 0 Reorder the terms: -4.3 + -3.7x + 2.5x2 = 0 Solving -4.3 + -3.7x + 2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -1.72 + -1.48x + x2 = 0 Move the constant term to the right: Add '1.72' to each side of the equation. -1.72 + -1.48x + 1.72 + x2 = 0 + 1.72 Reorder the terms: -1.72 + 1.72 + -1.48x + x2 = 0 + 1.72 Combine like terms: -1.72 + 1.72 = 0.00 0.00 + -1.48x + x2 = 0 + 1.72 -1.48x + x2 = 0 + 1.72 Combine like terms: 0 + 1.72 = 1.72 -1.48x + x2 = 1.72 The x term is -1.48x. Take half its coefficient (-0.74). Square it (0.5476) and add it to both sides. Add '0.5476' to each side of the equation. -1.48x + 0.5476 + x2 = 1.72 + 0.5476 Reorder the terms: 0.5476 + -1.48x + x2 = 1.72 + 0.5476 Combine like terms: 1.72 + 0.5476 = 2.2676 0.5476 + -1.48x + x2 = 2.2676 Factor a perfect square on the left side: (x + -0.74)(x + -0.74) = 2.2676 Calculate the square root of the right side: 1.505855239 Break this problem into two subproblems by setting (x + -0.74) equal to 1.505855239 and -1.505855239.Subproblem 1
x + -0.74 = 1.505855239 Simplifying x + -0.74 = 1.505855239 Reorder the terms: -0.74 + x = 1.505855239 Solving -0.74 + x = 1.505855239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.74' to each side of the equation. -0.74 + 0.74 + x = 1.505855239 + 0.74 Combine like terms: -0.74 + 0.74 = 0.00 0.00 + x = 1.505855239 + 0.74 x = 1.505855239 + 0.74 Combine like terms: 1.505855239 + 0.74 = 2.245855239 x = 2.245855239 Simplifying x = 2.245855239Subproblem 2
x + -0.74 = -1.505855239 Simplifying x + -0.74 = -1.505855239 Reorder the terms: -0.74 + x = -1.505855239 Solving -0.74 + x = -1.505855239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.74' to each side of the equation. -0.74 + 0.74 + x = -1.505855239 + 0.74 Combine like terms: -0.74 + 0.74 = 0.00 0.00 + x = -1.505855239 + 0.74 x = -1.505855239 + 0.74 Combine like terms: -1.505855239 + 0.74 = -0.765855239 x = -0.765855239 Simplifying x = -0.765855239Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.245855239, -0.765855239}
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