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Simplifying 10x2 + -3x + -40 = 0 Reorder the terms: -40 + -3x + 10x2 = 0 Solving -40 + -3x + 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 + -0.3x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.3x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -0.3x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.3x + x2 = 0 + 4 -0.3x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.3x + x2 = 4 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 4 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 4 + 0.0225 Combine like terms: 4 + 0.0225 = 4.0225 0.0225 + -0.3x + x2 = 4.0225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 4.0225 Calculate the square root of the right side: 2.005617112 Break this problem into two subproblems by setting (x + -0.15) equal to 2.005617112 and -2.005617112.Subproblem 1
x + -0.15 = 2.005617112 Simplifying x + -0.15 = 2.005617112 Reorder the terms: -0.15 + x = 2.005617112 Solving -0.15 + x = 2.005617112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 2.005617112 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 2.005617112 + 0.15 x = 2.005617112 + 0.15 Combine like terms: 2.005617112 + 0.15 = 2.155617112 x = 2.155617112 Simplifying x = 2.155617112Subproblem 2
x + -0.15 = -2.005617112 Simplifying x + -0.15 = -2.005617112 Reorder the terms: -0.15 + x = -2.005617112 Solving -0.15 + x = -2.005617112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -2.005617112 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -2.005617112 + 0.15 x = -2.005617112 + 0.15 Combine like terms: -2.005617112 + 0.15 = -1.855617112 x = -1.855617112 Simplifying x = -1.855617112Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.155617112, -1.855617112}
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