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Simplifying 3.7x2 + -7.5x + -4.2 = 2.7 Reorder the terms: -4.2 + -7.5x + 3.7x2 = 2.7 Solving -4.2 + -7.5x + 3.7x2 = 2.7 Solving for variable 'x'. Reorder the terms: -4.2 + -2.7 + -7.5x + 3.7x2 = 2.7 + -2.7 Combine like terms: -4.2 + -2.7 = -6.9 -6.9 + -7.5x + 3.7x2 = 2.7 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 -6.9 + -7.5x + 3.7x2 = 0.0 Begin completing the square. Divide all terms by 3.7 the coefficient of the squared term: Divide each side by '3.7'. -1.864864865 + -2.027027027x + x2 = 0 Move the constant term to the right: Add '1.864864865' to each side of the equation. -1.864864865 + -2.027027027x + 1.864864865 + x2 = 0 + 1.864864865 Reorder the terms: -1.864864865 + 1.864864865 + -2.027027027x + x2 = 0 + 1.864864865 Combine like terms: -1.864864865 + 1.864864865 = 0.000000000 0.000000000 + -2.027027027x + x2 = 0 + 1.864864865 -2.027027027x + x2 = 0 + 1.864864865 Combine like terms: 0 + 1.864864865 = 1.864864865 -2.027027027x + x2 = 1.864864865 The x term is -2.027027027x. Take half its coefficient (-1.013513514). Square it (1.027209643) and add it to both sides. Add '1.027209643' to each side of the equation. -2.027027027x + 1.027209643 + x2 = 1.864864865 + 1.027209643 Reorder the terms: 1.027209643 + -2.027027027x + x2 = 1.864864865 + 1.027209643 Combine like terms: 1.864864865 + 1.027209643 = 2.892074508 1.027209643 + -2.027027027x + x2 = 2.892074508 Factor a perfect square on the left side: (x + -1.013513514)(x + -1.013513514) = 2.892074508 Calculate the square root of the right side: 1.70061004 Break this problem into two subproblems by setting (x + -1.013513514) equal to 1.70061004 and -1.70061004.Subproblem 1
x + -1.013513514 = 1.70061004 Simplifying x + -1.013513514 = 1.70061004 Reorder the terms: -1.013513514 + x = 1.70061004 Solving -1.013513514 + x = 1.70061004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.013513514' to each side of the equation. -1.013513514 + 1.013513514 + x = 1.70061004 + 1.013513514 Combine like terms: -1.013513514 + 1.013513514 = 0.000000000 0.000000000 + x = 1.70061004 + 1.013513514 x = 1.70061004 + 1.013513514 Combine like terms: 1.70061004 + 1.013513514 = 2.714123554 x = 2.714123554 Simplifying x = 2.714123554Subproblem 2
x + -1.013513514 = -1.70061004 Simplifying x + -1.013513514 = -1.70061004 Reorder the terms: -1.013513514 + x = -1.70061004 Solving -1.013513514 + x = -1.70061004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.013513514' to each side of the equation. -1.013513514 + 1.013513514 + x = -1.70061004 + 1.013513514 Combine like terms: -1.013513514 + 1.013513514 = 0.000000000 0.000000000 + x = -1.70061004 + 1.013513514 x = -1.70061004 + 1.013513514 Combine like terms: -1.70061004 + 1.013513514 = -0.687096526 x = -0.687096526 Simplifying x = -0.687096526Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.714123554, -0.687096526}
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