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Simplifying -0.015x2 + 9.6x = 1400 Reorder the terms: 9.6x + -0.015x2 = 1400 Solving 9.6x + -0.015x2 = 1400 Solving for variable 'x'. Reorder the terms: -1400 + 9.6x + -0.015x2 = 1400 + -1400 Combine like terms: 1400 + -1400 = 0 -1400 + 9.6x + -0.015x2 = 0 Begin completing the square. Divide all terms by -0.015 the coefficient of the squared term: Divide each side by '-0.015'. 93333.33333 + -640x + x2 = 0 Move the constant term to the right: Add '-93333.33333' to each side of the equation. 93333.33333 + -640x + -93333.33333 + x2 = 0 + -93333.33333 Reorder the terms: 93333.33333 + -93333.33333 + -640x + x2 = 0 + -93333.33333 Combine like terms: 93333.33333 + -93333.33333 = 0.00000 0.00000 + -640x + x2 = 0 + -93333.33333 -640x + x2 = 0 + -93333.33333 Combine like terms: 0 + -93333.33333 = -93333.33333 -640x + x2 = -93333.33333 The x term is -640x. Take half its coefficient (-320). Square it (102400) and add it to both sides. Add '102400' to each side of the equation. -640x + 102400 + x2 = -93333.33333 + 102400 Reorder the terms: 102400 + -640x + x2 = -93333.33333 + 102400 Combine like terms: -93333.33333 + 102400 = 9066.66667 102400 + -640x + x2 = 9066.66667 Factor a perfect square on the left side: (x + -320)(x + -320) = 9066.66667 Calculate the square root of the right side: 95.219045731 Break this problem into two subproblems by setting (x + -320) equal to 95.219045731 and -95.219045731.Subproblem 1
x + -320 = 95.219045731 Simplifying x + -320 = 95.219045731 Reorder the terms: -320 + x = 95.219045731 Solving -320 + x = 95.219045731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '320' to each side of the equation. -320 + 320 + x = 95.219045731 + 320 Combine like terms: -320 + 320 = 0 0 + x = 95.219045731 + 320 x = 95.219045731 + 320 Combine like terms: 95.219045731 + 320 = 415.219045731 x = 415.219045731 Simplifying x = 415.219045731Subproblem 2
x + -320 = -95.219045731 Simplifying x + -320 = -95.219045731 Reorder the terms: -320 + x = -95.219045731 Solving -320 + x = -95.219045731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '320' to each side of the equation. -320 + 320 + x = -95.219045731 + 320 Combine like terms: -320 + 320 = 0 0 + x = -95.219045731 + 320 x = -95.219045731 + 320 Combine like terms: -95.219045731 + 320 = 224.780954269 x = 224.780954269 Simplifying x = 224.780954269Solution
The solution to the problem is based on the solutions from the subproblems. x = {415.219045731, 224.780954269}
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