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Simplifying 4.7x2 + 6.3x + -5.9 = 0 Reorder the terms: -5.9 + 6.3x + 4.7x2 = 0 Solving -5.9 + 6.3x + 4.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.7 the coefficient of the squared term: Divide each side by '4.7'. -1.255319149 + 1.340425532x + x2 = 0 Move the constant term to the right: Add '1.255319149' to each side of the equation. -1.255319149 + 1.340425532x + 1.255319149 + x2 = 0 + 1.255319149 Reorder the terms: -1.255319149 + 1.255319149 + 1.340425532x + x2 = 0 + 1.255319149 Combine like terms: -1.255319149 + 1.255319149 = 0.000000000 0.000000000 + 1.340425532x + x2 = 0 + 1.255319149 1.340425532x + x2 = 0 + 1.255319149 Combine like terms: 0 + 1.255319149 = 1.255319149 1.340425532x + x2 = 1.255319149 The x term is 1.340425532x. Take half its coefficient (0.670212766). Square it (0.4491851517) and add it to both sides. Add '0.4491851517' to each side of the equation. 1.340425532x + 0.4491851517 + x2 = 1.255319149 + 0.4491851517 Reorder the terms: 0.4491851517 + 1.340425532x + x2 = 1.255319149 + 0.4491851517 Combine like terms: 1.255319149 + 0.4491851517 = 1.7045043007 0.4491851517 + 1.340425532x + x2 = 1.7045043007 Factor a perfect square on the left side: (x + 0.670212766)(x + 0.670212766) = 1.7045043007 Calculate the square root of the right side: 1.305566659 Break this problem into two subproblems by setting (x + 0.670212766) equal to 1.305566659 and -1.305566659.Subproblem 1
x + 0.670212766 = 1.305566659 Simplifying x + 0.670212766 = 1.305566659 Reorder the terms: 0.670212766 + x = 1.305566659 Solving 0.670212766 + x = 1.305566659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.670212766' to each side of the equation. 0.670212766 + -0.670212766 + x = 1.305566659 + -0.670212766 Combine like terms: 0.670212766 + -0.670212766 = 0.000000000 0.000000000 + x = 1.305566659 + -0.670212766 x = 1.305566659 + -0.670212766 Combine like terms: 1.305566659 + -0.670212766 = 0.635353893 x = 0.635353893 Simplifying x = 0.635353893Subproblem 2
x + 0.670212766 = -1.305566659 Simplifying x + 0.670212766 = -1.305566659 Reorder the terms: 0.670212766 + x = -1.305566659 Solving 0.670212766 + x = -1.305566659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.670212766' to each side of the equation. 0.670212766 + -0.670212766 + x = -1.305566659 + -0.670212766 Combine like terms: 0.670212766 + -0.670212766 = 0.000000000 0.000000000 + x = -1.305566659 + -0.670212766 x = -1.305566659 + -0.670212766 Combine like terms: -1.305566659 + -0.670212766 = -1.975779425 x = -1.975779425 Simplifying x = -1.975779425Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.635353893, -1.975779425}
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