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Simplifying 99x2 + -7x + 5 = 100 Reorder the terms: 5 + -7x + 99x2 = 100 Solving 5 + -7x + 99x2 = 100 Solving for variable 'x'. Reorder the terms: 5 + -100 + -7x + 99x2 = 100 + -100 Combine like terms: 5 + -100 = -95 -95 + -7x + 99x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -95 + -7x + 99x2 = 0 Begin completing the square. Divide all terms by 99 the coefficient of the squared term: Divide each side by '99'. -0.9595959596 + -0.07070707071x + x2 = 0 Move the constant term to the right: Add '0.9595959596' to each side of the equation. -0.9595959596 + -0.07070707071x + 0.9595959596 + x2 = 0 + 0.9595959596 Reorder the terms: -0.9595959596 + 0.9595959596 + -0.07070707071x + x2 = 0 + 0.9595959596 Combine like terms: -0.9595959596 + 0.9595959596 = 0.0000000000 0.0000000000 + -0.07070707071x + x2 = 0 + 0.9595959596 -0.07070707071x + x2 = 0 + 0.9595959596 Combine like terms: 0 + 0.9595959596 = 0.9595959596 -0.07070707071x + x2 = 0.9595959596 The x term is -0.07070707071x. Take half its coefficient (-0.03535353536). Square it (0.001249872462) and add it to both sides. Add '0.001249872462' to each side of the equation. -0.07070707071x + 0.001249872462 + x2 = 0.9595959596 + 0.001249872462 Reorder the terms: 0.001249872462 + -0.07070707071x + x2 = 0.9595959596 + 0.001249872462 Combine like terms: 0.9595959596 + 0.001249872462 = 0.960845832062 0.001249872462 + -0.07070707071x + x2 = 0.960845832062 Factor a perfect square on the left side: (x + -0.03535353536)(x + -0.03535353536) = 0.960845832062 Calculate the square root of the right side: 0.980227439 Break this problem into two subproblems by setting (x + -0.03535353536) equal to 0.980227439 and -0.980227439.Subproblem 1
x + -0.03535353536 = 0.980227439 Simplifying x + -0.03535353536 = 0.980227439 Reorder the terms: -0.03535353536 + x = 0.980227439 Solving -0.03535353536 + x = 0.980227439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03535353536' to each side of the equation. -0.03535353536 + 0.03535353536 + x = 0.980227439 + 0.03535353536 Combine like terms: -0.03535353536 + 0.03535353536 = 0.00000000000 0.00000000000 + x = 0.980227439 + 0.03535353536 x = 0.980227439 + 0.03535353536 Combine like terms: 0.980227439 + 0.03535353536 = 1.01558097436 x = 1.01558097436 Simplifying x = 1.01558097436Subproblem 2
x + -0.03535353536 = -0.980227439 Simplifying x + -0.03535353536 = -0.980227439 Reorder the terms: -0.03535353536 + x = -0.980227439 Solving -0.03535353536 + x = -0.980227439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03535353536' to each side of the equation. -0.03535353536 + 0.03535353536 + x = -0.980227439 + 0.03535353536 Combine like terms: -0.03535353536 + 0.03535353536 = 0.00000000000 0.00000000000 + x = -0.980227439 + 0.03535353536 x = -0.980227439 + 0.03535353536 Combine like terms: -0.980227439 + 0.03535353536 = -0.94487390364 x = -0.94487390364 Simplifying x = -0.94487390364Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.01558097436, -0.94487390364}
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