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Simplifying 10x2 + 7x + -42 = 0 Reorder the terms: -42 + 7x + 10x2 = 0 Solving -42 + 7x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -4.2 + 0.7x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 0.7x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 0.7x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 0.7x + x2 = 0 + 4.2 0.7x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 0.7x + x2 = 4.2 The x term is 0.7x. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7x + 0.1225 + x2 = 4.2 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = 4.2 + 0.1225 Combine like terms: 4.2 + 0.1225 = 4.3225 0.1225 + 0.7x + x2 = 4.3225 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = 4.3225 Calculate the square root of the right side: 2.079062289 Break this problem into two subproblems by setting (x + 0.35) equal to 2.079062289 and -2.079062289.Subproblem 1
x + 0.35 = 2.079062289 Simplifying x + 0.35 = 2.079062289 Reorder the terms: 0.35 + x = 2.079062289 Solving 0.35 + x = 2.079062289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 2.079062289 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 2.079062289 + -0.35 x = 2.079062289 + -0.35 Combine like terms: 2.079062289 + -0.35 = 1.729062289 x = 1.729062289 Simplifying x = 1.729062289Subproblem 2
x + 0.35 = -2.079062289 Simplifying x + 0.35 = -2.079062289 Reorder the terms: 0.35 + x = -2.079062289 Solving 0.35 + x = -2.079062289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -2.079062289 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -2.079062289 + -0.35 x = -2.079062289 + -0.35 Combine like terms: -2.079062289 + -0.35 = -2.429062289 x = -2.429062289 Simplifying x = -2.429062289Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.729062289, -2.429062289}
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