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Simplifying 5x2 + -3x = 420 Reorder the terms: -3x + 5x2 = 420 Solving -3x + 5x2 = 420 Solving for variable 'x'. Reorder the terms: -420 + -3x + 5x2 = 420 + -420 Combine like terms: 420 + -420 = 0 -420 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -84 + -0.6x + x2 = 0 Move the constant term to the right: Add '84' to each side of the equation. -84 + -0.6x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + -0.6x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -0.6x + x2 = 0 + 84 -0.6x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 -0.6x + x2 = 84 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 84 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 84 + 0.09 Combine like terms: 84 + 0.09 = 84.09 0.09 + -0.6x + x2 = 84.09 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 84.09 Calculate the square root of the right side: 9.170059978 Break this problem into two subproblems by setting (x + -0.3) equal to 9.170059978 and -9.170059978.Subproblem 1
x + -0.3 = 9.170059978 Simplifying x + -0.3 = 9.170059978 Reorder the terms: -0.3 + x = 9.170059978 Solving -0.3 + x = 9.170059978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 9.170059978 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 9.170059978 + 0.3 x = 9.170059978 + 0.3 Combine like terms: 9.170059978 + 0.3 = 9.470059978 x = 9.470059978 Simplifying x = 9.470059978Subproblem 2
x + -0.3 = -9.170059978 Simplifying x + -0.3 = -9.170059978 Reorder the terms: -0.3 + x = -9.170059978 Solving -0.3 + x = -9.170059978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -9.170059978 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -9.170059978 + 0.3 x = -9.170059978 + 0.3 Combine like terms: -9.170059978 + 0.3 = -8.870059978 x = -8.870059978 Simplifying x = -8.870059978Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.470059978, -8.870059978}
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