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Simplifying 10x2 + -47x + -42 = 0 Reorder the terms: -42 + -47x + 10x2 = 0 Solving -42 + -47x + 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 + -4.7x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -4.7x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -4.7x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -4.7x + x2 = 0 + 4.2 -4.7x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -4.7x + x2 = 4.2 The x term is -4.7x. Take half its coefficient (-2.35). Square it (5.5225) and add it to both sides. Add '5.5225' to each side of the equation. -4.7x + 5.5225 + x2 = 4.2 + 5.5225 Reorder the terms: 5.5225 + -4.7x + x2 = 4.2 + 5.5225 Combine like terms: 4.2 + 5.5225 = 9.7225 5.5225 + -4.7x + x2 = 9.7225 Factor a perfect square on the left side: (x + -2.35)(x + -2.35) = 9.7225 Calculate the square root of the right side: 3.118092366 Break this problem into two subproblems by setting (x + -2.35) equal to 3.118092366 and -3.118092366.Subproblem 1
x + -2.35 = 3.118092366 Simplifying x + -2.35 = 3.118092366 Reorder the terms: -2.35 + x = 3.118092366 Solving -2.35 + x = 3.118092366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.35' to each side of the equation. -2.35 + 2.35 + x = 3.118092366 + 2.35 Combine like terms: -2.35 + 2.35 = 0.00 0.00 + x = 3.118092366 + 2.35 x = 3.118092366 + 2.35 Combine like terms: 3.118092366 + 2.35 = 5.468092366 x = 5.468092366 Simplifying x = 5.468092366Subproblem 2
x + -2.35 = -3.118092366 Simplifying x + -2.35 = -3.118092366 Reorder the terms: -2.35 + x = -3.118092366 Solving -2.35 + x = -3.118092366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.35' to each side of the equation. -2.35 + 2.35 + x = -3.118092366 + 2.35 Combine like terms: -2.35 + 2.35 = 0.00 0.00 + x = -3.118092366 + 2.35 x = -3.118092366 + 2.35 Combine like terms: -3.118092366 + 2.35 = -0.768092366 x = -0.768092366 Simplifying x = -0.768092366Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.468092366, -0.768092366}
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